Two moles of a monoatomic ideal gas is confined in a container and is heated such that its temperature increases by $10\,^{\circ}C$. The approximate change in its internal energy is ..... $J$. $(R = 8.31\, J/mol\cdot K)$

$A$ sample of an ideal gas is taken through the cyclic process $ABCA$ as shown in the figure. It absorbs $40 \ J$ of heat during the part $AB$,no heat during $BC$,and rejects $60 \ J$ of heat during $CA$. $A$ work of $50 \ J$ is done on the gas during the part $BC$. The internal energy of the gas at $A$ is $1560 \ J$. The work done by the gas during the part $CA$ is.............$J$.

$A$ monoatomic gas of $n$-moles is heated from temperature $T_1$ to $T_2$ under two different conditions: $(i)$ at constant volume and (ii) at constant pressure. The change in internal energy of the gas is

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4 \text{ cm}^2$. The gas is heated slowly to raise the temperature by $1.2^\circ\text{C}$ during which the piston moves by $25 \text{ mm}$. The amount of heat supplied to the gas is . . . . . . $J$. (Atmospheric pressure = $100 \text{ kPa}$, $R = 8.3 \text{ J/mol}\cdot\text{K}$) (Neglect mass of the piston)

$A$ cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in the figure.
$A$ to $B$: volume constant
$B$ to $C$: adiabatic
$C$ to $D$: volume constant
$D$ to $A$: adiabatic
$V_C = V_D = 2V_A = 2V_B$
$(a)$ In which part of the cycle is heat supplied to the engine from outside?
$(b)$ In which part of the cycle is heat given to the surrounding by the engine?
$(c)$ What is the work done by the engine in one cycle? Write your answer in terms of $P_A, P_B, V_A$.
$(d)$ What is the efficiency of the engine?
$(\gamma = 5/3, C_v = 3/2 R$ for one mole of the gas$)$

What is the specific heat of a gas in an isothermal process and an adiabatic process?