Question

1mole of oxygen initially at 7°c adiabatically compressed so that its pressure becomes 10 fold calculate its temperature after the compression, work done by the gas

Answer 1

For adiabatic process:

$$T_f=T_i(\frac{p_i}{p_f})^{\frac{1-\gamma}{\gamma}}$$

$$\frac{1-\gamma}{\gamma}=\frac{1-1.4}{1.4}=-\frac{2}{7}$$

$$T_i=273+7=280 K$$

$$\frac{p_i}{p_f}=\frac{1}{10}=0.1$$

$$T_f=280(0.1)^{-\frac{2}{7}}=540K$$

The work done by the gas:

$$W=\nu c_V (T_f-T_i)$$

$$W=(1)(21.1) (540-280)=5500 J=5.5 kJ$$