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 × 10^5 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 × 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}

A-Level AQA Physics Work, Energy & Power: Figure 1 shows a perfectly insul

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 calculate the specific heat capacity ( $c$ ) of liquid nitrogen, we first need to determine the total energy supplied to the nitrogen:

Total Energy Supplied ( $E_t$ ):

$E_t = P imes t = 12 ext{ W} imes 890 ext{ s} = 10680 ext{ J}$
Energy Required to Heat Liquid Nitrogen to Boiling Point:

Since we are heating the nitrogen from its initial temperature (70 K) to its boiling point (77 K), we will need to calculate the temperature difference ( $riangle T$ ).

$riangle T = 77 ext{ K} - 70 ext{ K} = 7 ext{ K}$
Calculate the Specific Heat Capacity ( $c$ ):

The specific heat capacity can be calculated using the formula:

$c = rac{E}{m imes riangle T}$

Where,
- $E$ = total energy supplied = 10680 J
- $m$ = mass of nitrogen = 0.050 kg
Substituting the values:

$c = rac{10680 ext{ J}}{0.050 ext{ kg} imes 7 ext{ K}} = rac{10680}{0.35} ext{ J kg}^{-1} ext{ K}^{-1} = 30514.29 ext{ J kg}^{-1} ext{ K}^{-1}$

Therefore, the specific heat capacity of liquid nitrogen is approximately 30500 J kg^{-1} K^{-1}.

Step 2

Determine Work Done (X) and Energy Required (Y)

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Answer

Work Done by Nitrogen ( $X$ ):

The work done by the nitrogen during expansion can be calculated using the formula:

$X = P imes riangle V$

Assuming an approximate volume change with negligible contributions and density considerations, calculate accordingly when the change state occurs from liquid to gas.
Energy Required to Change State ( $Y$ ):

The energy required for the phase change of nitrogen from a liquid to a gas is given by the specific latent heat of vaporization:

$Y = m imes L = 0.050 ext{ kg} imes 2.0 imes 10^5 ext{ J kg}^{-1} = 10000 ext{ J}$
Compare X and Y:

Given that the density of the gas at the boiling point (3.8 kg m^{-3}) is significantly lower than that of the liquid (810 kg m^{-3}), it can be inferred that the volume change during the state transition may lead to greater instantaneous work done ( $W ightarrow X$ being nearly negligible compared to $Y$ ). Hence,

$X < Y$ Thus the energy required to change the state of nitrogen is greater than the work done during the process.

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

Determine Work Done (X) and Energy Required (Y)

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