When 1 text{ mole} of an ideal gas (gamma = 1 | vedclass

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(B) The change in internal energy $(\Delta U)$ for an ideal gas is given by the formula: $\Delta U = n C_v \Delta T$. For an ideal gas,$C_v = \frac{R}

Vedclass · Accepted Answer

$166$

Vedclass · Answer

(B) The change in internal energy $(\Delta U)$ for an ideal gas is given by the formula: $\Delta U = n C_v \Delta T$. For an ideal gas,$C_v = \frac{R}{\gamma - 1}$. Given: $n = 1 	ext{ mole}$,$\gamma = 1.4$,$R = 8.3 	ext{ J/mol K}$,$T_1 = 27^{\circ}C$,$T_2 = 35^{\circ}C$. Change in temperature $\Delta T = T_2 - T_1 = 35 - 27 = 8 	ext{ K}$. Substituting the values: $\Delta U = 1 	imes \frac{8.3}{1.4 - 1} 	imes 8$. $\Delta U = \frac{8.3}{0.4} 	imes 8 = 8.3 	imes 20 = 166 	ext{ J}$. Thus,the increase in internal energy is $166 	ext{ J}$.

When $1 \text{ mole}$ of an ideal gas $(\gamma = 1.4)$ is compressed adiabatically,its temperature increases from $27^{\circ}C$ to $35^{\circ}C$. The increase in the internal energy of the gas is ...... $J$? $(R = 8.3 \text{ J/mol K})$

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