Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K. A heater transfers energy at a constant rate of 12 W to the nitrogen. A piston maintains the pressure at 1.0 x 10^6 Pa during the heating process. The nitrogen is heated from 70 K and is completely turned into a gas after 890 s. Calculate the specific heat capacity of liquid nitrogen. Give an appropriate unit for your answer. specific latent heat of vaporisation of nitrogen = 2.0 x 10^5 J kg^-1 boiling point of nitrogen = 77 K [5 marks] The work done by the nitrogen in the cylinder when expanding due to a change of state is X. The energy required to change the state of the nitrogen from a liquid to a gas is Y. Deduce which is greater, X or Y. - density of liquid nitrogen at its boiling temperature = 810 kg m^-3 - density of nitrogen gas at its boiling temperature = 3.8 kg m^-3

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Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K - AQA - A-Level Physics - Question 1 - 2019 - Paper 2

Question 1

Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K. A heater transfers energy at a constant rate of 12 W t... show full transcript

Worked Solution & Example Answer:Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K - AQA - A-Level Physics - Question 1 - 2019 - Paper 2

Step 1

Calculate the specific heat capacity of liquid nitrogen.

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Answer

To find the specific heat capacity of liquid nitrogen, we first calculate the total energy supplied by the heater:

$ext{Total Energy} (Q) = P imes t = 12 ext{ W} imes 890 ext{ s} = 10680 ext{ J}$

Next, we apply the formula for heat energy: $Q = mc(T_f - T_i)$ which leads us to: $c = \frac{Q}{m(T_f - T_i)}$ Here, the mass (m) of liquid nitrogen is 0.050 kg, the initial temperature (T_i) is 70 K, and the final temperature (T_f) at the boiling point is 77 K:

Substituting the known values: $c = \frac{10680 ext{ J}}{0.050 ext{ kg} (77 ext{ K} - 70 ext{ K})} = \frac{10680 ext{ J}}{0.050 ext{ kg} imes 7 ext{ K}} = \frac{10680 ext{ J}}{0.35 ext{ kg K}} = 30514.29 ext{ J kg}^{-1} ext{ K}^{-1}$

Thus, the specific heat capacity of liquid nitrogen is approximately 30514.29 J kg^-1 K^-1.

Step 2

The work done by the nitrogen in the cylinder when expanding due to a change of state is X.

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Answer

To find X, we utilize the equation for work done by the gas: $X = P imes \Delta V$ As the volume change (\Delta V) is negligible for a liquid transitioning to a gas, we consider the relationship of energy and state change in this case.

Given that the density of liquid nitrogen at its boiling point is 810 kg m^-3 and the density of nitrogen gas at its boiling temperature is 3.8 kg m^-3, we can calculate the volumes. The work done is primarily related to the vast increase in volume during the phase change. Thus: $X = P \times \Delta V$ But since the volume change is substantial due to the gaseous state, we confirm that the expansion work being negligible doesn’t affect the conclusion significantly.

Step 3

The energy required to change the state of the nitrogen from a liquid to a gas is Y.

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Answer

To calculate Y, we utilize the latent heat formula: $Y = mL$ Where:

m = 0.050 kg (mass of nitrogen)
L = 2.0 x 10^5 J kg^-1 (specific latent heat of vaporization)

Thus: $Y = 0.050 ext{ kg} imes 2.0 imes 10^5 ext{ J kg}^{-1} = 10000 ext{ J}$

Step 4

Deduce which is greater, X or Y.

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Answer

From the calculations, we see that:

X is related to the work done during expansion, which given the negligible volume change is not significant.
Y, being the total energy required to change the state from liquid to gas is calculated as 10000 J.

Thus, since $X$ does not contribute significantly while $Y$ is a definite quantity, it can be concluded that: $Y > X$

Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K - AQA - A-Level Physics - Question 1 - 2019 - Paper 2

Worked Solution & Example Answer:Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K - AQA - A-Level Physics - Question 1 - 2019 - Paper 2

Calculate the specific heat capacity of liquid nitrogen.

The work done by the nitrogen in the cylinder when expanding due to a change of state is X.

The energy required to change the state of the nitrogen from a liquid to a gas is Y.

Deduce which is greater, X or Y.

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