The First Law of Thermodynamics (CIE A Level Physics)

Fig. 1.1 shows a chamber containing 5.2 kg of a gas, with a 0.75 kg piston above the gas.

Fig. 1.1

When the gas is supplied with 32.4 kJ of heat, the piston experiences an average upwards acceleration 3.5 m s⁻² over a distance of 12 cm.

Calculate the work done by the gas.

Later, the piston is fixed in place and is unable to move. The gas is supplied with the same amount of heat. Its temperature raises by 20 K.

Calculate the specific heat capacity of the gas at a constant volume, C_V .

Calculate the relative atomic mass of the gas within the piston chamber.

You may use the following equation for the change in internal energy for an ideal gas:

where n  is the number of moles of gas in the system, R  is the molar gas constant and ΔT  is the change in temperature, in kelvin.

Define the work done by a gas.

A mass of water with negligible volume is vapourised into water vapour of volume 0.82 m³ at a temperature of 100 °C and atmospheric pressure 1.0 × 10⁵ Pa. The thermal energy supplied to the water is 9.5 × 10⁵ J. 

Calculate the magnitude of the work done by the water in expanding against the atmosphere when it vapourises. 

Determine the increase in internal energy of the water when it vapourises at 100 °C. Explain your reasoning.

Suggest, with a reason, how the specific latent heat of vapourisation of water at a pressure greater than atmospheric pressure compares with its value at atmospheric pressure.

State the first law of thermodynamics and include any relevant units.

A fixed mass of water is in a beaker at atmospheric pressure. The initial temperature of the water is 0 °C. The water is supplied with thermal energy q, so that its temperature increases to 10 °C. There is no net change in the volume of the water. 

Determine the work done and the increase in internal energy of the water by completing Table 1.1, considering the first law of thermodynamics.

Table 1.1

The water from part (b) is now heated so it's temperature increases by a further 10 °C to a final temperature of 20 °C. This process causes the volume of the water to increase so that work W is done.

Assume that the change in internal energy is the same as in part (b). 

Determine the work done, thermal energy supplied and the increase in internal energy of the water by completing Table 1.2, considering the first law of thermodynamics.

Table 1.2

Explain how the average specific heat capacity of the water, in parts (b) and (c), between 10 °C and 20 °C compares with its average value between 0 °C and 10 °C.