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The coefficients of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$, lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained the same at all temperatures, which one of the following relations holds good?
Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively, the effective conductivity of the combination is:
A metal wire has mass $(0.4 \pm 0.002)$ g, radius $(0.3 \pm 0.001)$ mm and length $(5 \pm 0.02)$ cm. The maximum possible percentage error in the measurement of density will nearly be
The net magnetic flux through any closed surface is
A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod when placed in thermal contact with the two reservoirs in time $t$?
A cup of coffee cools from $90^{\circ}\text{C}$ to $80^{\circ}\text{C}$ in $t$ minutes, when the room temperature is $20^{\circ}\text{C}$. The time taken by a similar cup of coffee to cool from $80^{\circ}\text{C}$ to $60^{\circ}\text{C}$ at room temperature same at $20^{\circ}\text{C}$ is:
A sample of $0.1 \text{ g}$ of water at $100^{\circ}\text{C}$ and normal pressure ($1.013 \times 10^5 \text{ N m}^{-2}$) requires $54 \text{ cal}$ of heat energy to convert it into steam at $100^{\circ}\text{C}$. If the volume of the steam produced is $167.1 \text{ cc}$, then the change in internal energy of the sample will be:
Thermodynamic processes are indicated in the following diagram. Match the following: Column I P. Process I Q. Process II R. Process III S. Process IV Column II a. Adiabatic b. Isobaric c. Isochoric d. Isothermal
The efficiency of an ideal heat engine (Carnot heat engine) working between the freezing point and boiling point of water is:
The molar specific heat at a constant pressure of an ideal gas is $(7/2)R$. The ratio of specific heat at constant pressure to that at constant volume is:
The temperature inside a refrigerator is $t_2^\circ\text{C}$ and the room temperature is $t_1^\circ\text{C}$. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be:
A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:
If $Q$, $E$ and $W$ denote respectively the heat added, change in internal energy and the work done in a closed cyclic process, then
An ideal gas is compressed to half its initial volume by means of several processes. Which of the following processes results in the maximum work being done on the gas?
A thermodynamic system undergoes a cyclic process $ABCDA$ as shown in Fig. The work done by the system in the cycle is:
A thermodynamic system undergoes cyclic process ABCDA as shown in figure. The work done by the system in the cycle is:
A thermodynamic system is taken through the cycle ABCD as shown in the figure. Heat rejected by the gas during the cycle is:
The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_P$ and $C_V$, respectively. If $\gamma = \frac{C_P}{C_V}$ and $R$ is the universal gas constant, then $C_V$ is equal to:
The dimensional formula for impulse is:
One mole of an ideal gas goes from an initial state $A$ to the final state $B$ with two processes. It first undergoes isothermal expansion from volume $V$ to $3V$ and then its volume is reduced from $3V$ to $V$ at constant pressure. The correct $(P-V)$ diagram representing the two processes is: