Question 2
2
the rise in temperature of the gas. temperature rise = K
structured2 marks
Question 2(a)
2(a)
The volume of an ideal gas in a cylinder is \(1.80 \times 10^{-3} \mathrm{~m}^{3}\) at a pressure of \(2.60 \times 10^{5} \mathrm{~Pa}\) and a temperature of 297 K , as illustrated in Fig. 2.1. The thermal energy required to raise the temperature by 1.00 K of 1.00 mol of the gas at constant volume is 12.5 J . The gas is heated at constant volume such that the internal energy of the gas increases by 95.0 J .
structured1 marks
Question 2(a)(i)
2(a)(i)
Calculate
Mediumstructured0 marks
Answer
1. p V=n R T \(1.80 \times 10^{-3} \times 2.60 \times 105=n \times 8.31 \times 297 \quad\) C1 \(n=0.19 \mathrm{~mol}\) A1 2. \(\Delta q=m c \Delta T\) \(95.0=0.190 \times 12.5 \times \Delta T\) B1 \(\Delta T=40 \mathrm{~K}\) A1 (allow 2 marks for correct answer with clear logic shown)
Question 2(a)(ii)
2(a)(ii)
Use your answer in (i) part 2 to show that the final pressure of the gas in the cylinder is \(2.95 \times 10^{5} \mathrm{~Pa}\).
Mediumstructured1 marks
Answer
p / T= constant \(\left(2.6 \times 10^{5}\right) / 297=p /(297+40)\) \(p=2.95 \times 10^{5} \mathrm{~Pa}\)
Question 2
2
A cylinder contains 5.12 mol of an ideal gas at pressure \(5.60 \times 10^{5} \mathrm{~Pa}\) and volume \(3.80 \times 10^{-2} \mathrm{~m}^{3}\).
structured3 marks
Question 2(a)
2(a)
Calculate the thermodynamic temperature of the gas.
Easystructured2 marks
Answer
p V=n R T C1 \[ \begin{aligned} T=\left(5.60 \times 10^{5} \times 3.80 \times 10^{-2}\right) /(5.12 \times 8.31) T=500 \mathrm{~K} \end{aligned} \] A1
Question 2(b)
2(b)
The average kinetic energy \(E_{\mathrm{K}}\) of a molecule of the gas is given by the expression where k is the Boltzmann constant and T is the thermodynamic temperature. The gas is heated at constant pressure so that its temperature rises by 125 K .
structured1 marks
Question 2(b)(i)
2(b)(i)
Show that the new volume of the gas is \(4.75 \times 10^{-2} \mathrm{~m}^{3}\).
Mediumstructured1 marks
Answer
\(V=\left(3.80 \times 10^{-2}\right) \times(500+125) / 500=4.75 \times 10^{-2} \mathrm{~m}^{3}\) A1
Question 2
2
A constant mass of an ideal gas has a volume of \(3.49 \times 10^{3} \mathrm{~cm}^{3}\) at a temperature of \(21.0^{\circ} \mathrm{C}\). When the gas is heated, 565 J of thermal energy causes it to expand to a volume of \(3.87 \times 10^{3} \mathrm{~cm}^{3}\) at \(53.0^{\circ} \mathrm{C}\). This is illustrated in Fig.2.1.
structured2 marks
Question 2(a)
2(a)
Show that the initial and final pressures of the gas are equal.
Mediumstructured2 marks
Answer
use of kelvin temperatures both values of (V / T) correct (11.87), V / T is constant so pressure is constant (allow use of n=1. Do not allow other values of n.)