Juan Hewlett

2022-01-06

0.250 kilogram of water at ${75.0}^{\circ}C$ are contained in a tiny, inert beaker. How much ice, at a temperature of $-{20.0}^{\circ}C$ degrees, needs to be added to the water to reach the desired temperature of ${40.0}^{\circ}C$ degrees?

Jacob Homer

Beginner2022-01-07Added 41 answers

The final temperature of the system is $40{C}^{\circ}$ and the total heat flow for the system will be Zero.

${Q}_{\to tal}={Q}_{ice}+{Q}_{water}=0$ (1)

The ice will go through three stages, so you need to be careful while you are calculating$Q}_{ice$ , the first stage includes the change of the temperature of the ice but without any change in the phase ''''it still solid through this stage”, the second stage starts when the ice reaches its melting point and ends when the all the ice melts, the final stage includes the changing of the temperature of the water that was ice before melting, meaning that this water has the same mass as the ice. Hence, $Q}_{ice$ can be written as follows

$Q}_{ice}={m}_{ice}\times {c}_{ice}\times \mathrm{\u25b3}{T}_{ice}+{m}_{ice}\times {L}_{f}+{m}_{ice}\times {c}_{water}\times \mathrm{\u25b3}{T}_{me<ed$

Substitute for the quantities in the above equation to get$Q}_{ice$

${Q}_{ice}={m}_{ice}[(2100\frac{J}{kg}\cdot C\xb0)\times [0-(-20C\xb0)]+(33.4\times {10}^{4}\frac{J}{kg})+(4190\frac{J}{kg}\cdot C\xb0)\times (40C\xb0-0)]$

$Q}_{ice}=[5.436\times {10}^{5}\frac{J}{kg}]{m}_{ice$

Now, let's calculate Q for the water which has a mass of (0.25 kg) and its temperature drops from 75C° to 40C°

${Q}_{water}={m}_{water}\times {c}_{water}\times \mathrm{\u25b3}T$

${Q}_{water}=\left(0.25kg\right)\times (4190\frac{J}{kg}\cdot C\xb0)\times (40C\xb0-75C\xb0)$

${Q}_{water}=-3.67\times {10}^{4}J$

Now, to get the value of mice, substitute for$Q}_{water$ and $Q}_{ice$ into eq.(1)

$[5.436\times {10}^{5}J]{m}_{ice}-3.67\times {10}^{4}\frac{J}{kg}=0$

$m}_{ice}=\frac{3.67\times {10}^{4}J}{5.436x{10}^{5}\frac{J}{kg}$

${m}_{ice}=0.0675kg$

The ice will go through three stages, so you need to be careful while you are calculating

Substitute for the quantities in the above equation to get

Now, let's calculate Q for the water which has a mass of (0.25 kg) and its temperature drops from 75C° to 40C°

Now, to get the value of mice, substitute for

Maricela Alarcon

Beginner2022-01-08Added 28 answers

Required

the mass of the

Given

Solution

Final temperature be

So the thermal heat of the system

Where

and

by solving equation (1)

0

karton

Expert2022-01-10Added 613 answers

Explanation:

Heat gained by ice in taking the total temperature to

Total Heat gained by

Heat used to melt at

To do this, we require the specific heat capacity of ice, latent heat of ice and the specific heat capacity of water. All will be obtained from literature.

Specific heat capacity of

Latent heat of

Specific heat capacity of

Heat gained by ice in taking the total temperature to

Heat lost by

543600m=36627.5

m=0.0674kg=67.4g of ice.

22+64

When a cold drink is taken from a refrigerator, its temperature is 5 degree C. After 25 minutes in a 20 degree C room its temperature has increased to 10 degree C. What is the temperature of the drink after 50 minutes?

How many minutes are there in $2\frac{3}{5}$ hours?

Find the answer for $64$ power $\frac{1}{6}$.

The following law describes the relationship between gas volume and pressure: ________. A)Boyle's law; B)Henry's law; C)Charles' law; D)Dalton's law

If an electric switch is open then no current flows through the circuit.

A)True;

B)FalseThe price elasticity of supply of a good is 0.8. Its price rises by 50 per cent. Calculate the percentage increase in its supply.

How many quarts are in 10 gallons?

When the net force acting on an object is zero, the total momentum of the system will:

A)remain constant;

B)increase with time;

C)decrease with time;

D)None of theseHow many centimeters are in four meters?

A notebook computer has a mass of 2.25 kilograms. About how many pounds does the notebook weigh?

If the dot product of two non-zero vectors is zero, then the vectors A)are parallel to each other. B)are perpendicular to each other. C)can have any orientation. D)are anti-parallel to each other.

Which is longer 5 miles or 10 kilometers?

9 grams is how many milligrams?

How to write $673.5$ in scientific notation?