Question

A mass of gas was compressed without friction at constant pressure of 100 kPa from $0.3m^3$ of initial state to the $0.15m^3$ of final state.
There was a transfer of 48 kJ. of heat from the gas during the process. The decrease in internal energy of the gas is

• A. 33 kJ
• B. -33 kJ
• C. 28.5 kJ
• D. 42 kJ

Answer 1

The correct option is A 33 kJ

$\text{Initial state:}{P}_1=100kPa,V_1=0.3m^3$
$\text{Final state:}{P}_2=100kPa,V_2=0.15m^3$
$\begin{array}{ccc}Q& =-48kJ& \\ \text{Now}& & \\ Q_{1-2}& =\Delta U+W_{1-2}& \dots \dots \left(1\right)\\ W_{1-2}& ={\int }_{v_1}^{v_2}PdV& \\ & =-100\times (0.3-0.15)=-15kJ& \\ \text{From eq . (1)}& & \\ U_2-U_1& =-48+15=-33kJ& \\ \text{Decrease in internal energy}& =33kJ& \end{array}$