Thermal Physics Q&A: Get Expert Help and Learn from Real-World Examples

Final temperature of a mixture of water and ice in a copper container
Lets say I have ice of mass $m_i$ and initial temperature $T_i$ and specific heat $s_i$ . And I have water of mass $m_w$ and initial temperature $T_w$ and specific heat $s_w$ . I have put both this water and ice in a copper container with mass $m_{cu}$ , specific heat $s_{cu}$ and initial temperature $T_w$ . What will be the final temperature $T$ of the system ? ( The Latent heat of freezing of water is $L_f$ )
Here ,
$Q_1=m_i{s}_i(T-<!--\; -\; -->T_i)+m_i{L}_f$
$Q_2=m_w{s}_w(T-<!--\; -\; -->T_w)+m_w{L}_f+m_{cu}{s}_{cu}(T-<!--\; -\; -->T_w)$
According to Calorimetry ,
$Q_1=Q_2$
$m_i{s}_i(T-<!--\; -\; -->T_i)+m_i{L}_f=Q_2=m_w{s}_w(T-<!--\; -\; -->T_w)+m_w{L}_f+m_{cu}{s}_{cu}(T-<!--\; -\; -->T_w)$
I can use this equation to calculate $T$ , But then I ran into a problem. In this case , I don't know which is happening , the freezing of water , or the melting of ice , so i can't just put both $m_w{L}_f$ and $m_i{L}_f$ in the equation and call it done. I might have to remove one of them depending on which thing is not happening (freezing or melting) .To make matters worse , The water or ice may just freeze or melt partially. Is there another equation that can solve for the final temperature while also taking all of this into account?

If the Helmholtz energy of a reaction is closed system is positive (at constant Volume and Temperature) what does this indicate about the corresponding change in total entropy of the system + surrounding?
a) It is negative
b) It is positive
c) It is equal to 0
d) It depends on the value of the enthalpy of the reaction
e) None of the above

Entropy change in a calorimetry problem
A standard textbook problem has us calculate the change in entropy in a system that undergoes some sort of heat exchange. For example, object $A$ has specific heat $c_a$ and initial temperature $T_A$ and object $B$ has specific heat $c_b$ with initial temperature $T_B$. They are they put in contact with each other until they reach thermal equilibrium, and our goal is to find the total entropy change of the system.
The standard solution is to use
$S=\int <!--\; \int \; -->\frac{dQ}{T}$
where $dQ=mcdT$. But the above integral is only satisfied for reversible processes, whereas this heat exchange is clearly irreversible.
The usual workaround for this is to pick some reversible path and calculate the entropy change on our "fake" path, since entropy is a state variable. For example, in the free expansion of an ideal gas, we pick calculate the entropy change along an isotherm that carries us along the expansion to find the true change in entropy.
My question is - what exactly is the reversible path we are using when we use $dQ=mcdT$?

What is the effect of pressure on the fusion and boiling point of water?

A mole of a van der Waals gas is expanded isothermally from $V_1$ to $V_2$. Derive the expressions for the changes in the Helmholtz free energy and internal energy.

Which of the following is a vector: a person’s height, the altitude on Mt. Everest, the age of the Earth, the boiling point of water, the cost of this book, the Earth’s population, the acceleration of gravity?

Which will boil first? Assuming all variables are constant.
- Water in airplane at altitude of 20000 feet.
- Water in ship.
- Water near seashore.
- all of these will boil at same temperature

a) How many degrees are between the melting point of ice and boiling point of water on the Celsius scale? b) Fahrenheit scale?

To determine:
The relationship of the boiling point and the altitude in the form of T=mx+b

The temperature at which water boils at an altitude of 4000 feet.

Infer from a standard free energy change whether a reaction is exergonic or endergonic

A constant-volume gas thermometer filled with air whose pressure is 101kPa at the normal melting point of ice. What would its pressure be at the normal point boiling of water (373K) ?

On a linear X temperature scale, water freezes at $-<!--\; -\; -->{125.0}^{0}X$ and boils at ${360.0}^{0}X$. On a linear Y scale, water freezes at $-<!--\; -\; -->{70.00}^{0}Y$ and boils at $-<!--\; -\; -->{30.00}^{0}Y$. A temperature of ${50.00}^{0}Y$ corresponds to what temperature on the X scale?

Heat transfer vs calorimetry equation
I'm trying to understand the difference between the equations
$Q=mc\mathrm{\Delta <!--\; \Delta \; -->}T$
and,
$\frac{dQ}{dt}=\frac{-<!--\; -\; -->\mathrm{\kappa <!--\; \kappa \; -->}\mathrm{\alpha <!--\; \alpha \; -->}\mathrm{\Delta <!--\; \Delta \; -->}T}{l}$
Suppose, we have two metal rods at $T_1$ and $T_2$ temperature, and we connect them at the end. I want to know, what do the two above equations tell us, regarding this system.
My understanding is that the first equation tells us, that the two systems will reach an equilibrium temperature, and the heat gained by one rod would be the heat lost by the other. This final temperature would depend upon the relative masses, and heat capacities. However, the first equation tells us, how much heat flows out of the first rod, into the second rod, and the final temperature.
Where does this second equation come from, and what does it tell us ? It seems to me, that the second equation would give us the heat transferred from one rod to the other, in some given time, unlike the first one that gives us the total heat transferred.
Combining the two above equations, we can derive the partial differential equation, called the heat equation. My question is, what does my heat equation tell me ? The first equation tells me, the final temperature of two bodies in contact, provided I know the initial temperature, mass and heal capacities.
What does the heat/diffusion equation tell me then ? Does it tell me, the distribution of heat at some given time ?
Does it mean, if I use the heat equation for our problem with the two rods at different temperatures, I'd get the same final temperature as the $Q=mc\mathrm{\Delta <!--\; \Delta \; -->}T$ equation, after some time, and this temperature would be constant ?

Entropy change is defined as the amount of energy dispersed reversibly to or from the system at a specific temperature. Reversivility means that the temperature of the system must remain constant during the dispersal of energy to or from the system . But this criterion is only fulfilled during phase change & isothermal processes. But not all processes maintain constant temperature;temperature may change constantly during the dispersal of energy to or from the system . To measure entropy change ,say, from $300K$ & $310K$, the range is divided into infinitesimal ranges ,then entropy is measured in that ranges and then is integrated . But I cannot understand how they have measured entropy change in that infinitesimal ranges as there will always be difference between the temperature however small the range might be . What is the intuition behind it? Change of entropy is measured at constant temperature,so how can it be measured in a range ? I know it is done by definite integration but can't getting the proper intuition . Also ,if by using definite integration to measure change, continuous graph must be there(like to measure change in velocity,area under the graph of acceleration is measured) . So what is the graph whose area gives change in entropy? Plz help me explaining these two questions.

Explain why on addition of 1 mol of NaCl to 1 litre of water, the boiling point of water increases, while addition of 1 mol of methyl alcohol to one litre of water decreases its boiling point.

Water boils at ${100}^{\circ <!--\; \circ \; -->}C$ at atmospheric pressure, that is, at sea level $(T^{\circ <!--\; \circ \; -->}={15}^{\circ <!--\; \circ \; -->}C)$. The boiling point is defined as the temperature at which the vapor pressure of water is equal to the atmospheric pressure. This has consequences for cooking in places such as Atok where it takes quite a bit longer to make a hard-boiled egg than it would in Baguio City. If the albumen in an egg needs to reach ${75}^{\circ <!--\; \circ \; -->}C$ for the protein to coagulate, at what height would it be impossible to hard boil an egg?

Why might you expect the canonical partition function to scale exponentially with the system size, thus always ensuring that the Helmholtz free energy is extensive?

Spin 1/2 particles in magnetic Field B can take energies $E=\pm <!--\; \pm \; -->{\mathrm{\mu <!--\; \mu \; -->}}_{B}B$
a) For N non interacting spin -1/2 particles at temperature T, derive the partition function Z and Helmholtz free energy F.
b) Calculate the magnetic moment of this system, given by $m=-<!--\; -\; -->(\frac{\mathrm{\partial <!--\; \partial \; -->}F}{\mathrm{\partial <!--\; \partial \; -->}B}{)}_T$

If a solute is non-volatile, its water solution boils at a temperature below the boiling point of water. This statement is:
A. valid
B. possible for all gases
C. true
D. false