$A$ sample of an ideal gas undergoes an isothermal expansion. If $dQ$,$dU$,and $dW$ represent the amount of heat supplied,the change in internal energy,and the work done respectively,then:

  • A
    $dQ = +ve, dU = +ve, dW = +ve$
  • B
    $dQ = +ve, dU = 0, dW = +ve$
  • C
    $dQ = +ve, dU = +ve, dW = 0$
  • D
    $dQ = -ve, dU = -ve, dW = -ve$

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$A$ poly-atomic molecule $(C_v = 3R, C_p = 4R$,where $R$ is the gas constant) goes from phase space point $A (P_A = 10^5 \ Pa, V_A = 4 \times 10^{-6} \ m^3)$ to point $B (P_B = 5 \times 10^4 \ Pa, V_B = 6 \times 10^{-6} \ m^3)$ and then to point $C (P_C = 10^4 \ Pa, V_C = 8 \times 10^{-6} \ m^3)$. The path $A$ to $B$ is adiabatic and the path $B$ to $C$ is isothermal. The net heat absorbed per unit mole by the system is:

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