D. C. Pandey Solutions for Chapter: The First Law of Thermodynamics, Exercise 1: Objective Problems

A Carnot engine whose efficiency is $40\%,$ receives heat at $500 \mathrm{K}$. If the efficiency is to be $50\%$, the source temperature for the same exhaust temperature is

$100 \mathrm{g}$ of water is heated from $30 °\mathrm{C}$ to $50 °\mathrm{C}$. Ignoring the slight expansion of the water, the change in its internal energy is (Specific heat of water is $4184 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

The thermodynamic process in which no work is done on or by the gas is

Two soap bubbles of radii $x$ and $y$ coalesce to constitute bubble of radius $z$. Then, $z$ is equal to

A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_{\mathrm{i}}$ (in kelvin) and the final temperature is $T_{\mathrm{f}}=a{T}_{\mathrm{i}}$, then value of $a$ is

A diatomic ideal gas is used in a car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from $V$ to $32 \mathrm{V}$. The efficiency of the engine is

The efficiency of a Carnot engine working between $800 \mathrm{K}$ and $500 \mathrm{K}$ is

The efficiency of Carnot heat engine is $0.5$, when the temperature of the source is $T_1$ and that of sink is $T_2$. The efficiency of another Carnot heat engine is also $0.5$. The temperatures of source and sink of the second engine respectively are