Thermodynamics practice · Mixed difficulty

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer from the options given below

For two substance ratio of mass is $1: 2$ and ratio of specific heat is 2 : 3 and its temperature is $10^{\circ} \mathrm{C}$ and $40^{\circ} \mathrm{C}$ respectively then find out the temperature of mixture.

An engine operating between the boiling and freezing points of water will have
A. Efficiency more than $27 \%$
B. Efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.
C. Efficiency equal to $27\%.$
D. Efficiency less than $27\%.$
Choose the correct answer from the options given below

During the adiabatic expansion of 2 moles of a gas, change in internal energy was found to be equal to 100 J. Work done in the process will be equal to

A cycle pump becomes hot near the nozzle after a few quick strokes even if they are smooth because

In thermodynamic processes which of the following statements is not true

One mole of an ideal gas expands at a constant temperature of $300K$ from an initial volume of $10\,\,\,litres$to a final volume of $20\,\,\,litres$. The work done in expanding the gas is $(R = 8.31J/mole - K)$

Assertion: Two isothermal curves intersect each other at a certain point.
Reason: The isothermal change are done slowly, so the isothermal curves have very little slope.

For an ideal gas, in an isothermal process

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

Assertion: Straight line on $p-T$ graph for an ideal gas represents isochoric process.

Reason: If $p \propto T, V=$ constant.

In an isothermal change of an ideal gas, $\Delta U = 0$. The change in heat energy $\Delta Q$ is equal to

A gas expands under constant pressure P from volume ${V_1}$ to ${V_2}$. The work done by the gas is

A gas expands adiabatically at constant pressure, such that its temperature $\propto \frac{1}{{\sqrt V .}}$) . The value of ${C_p}/{C_v}$of the gas is

Given below are two statements
Statement-I: When $\mu$ amount of an ideal gas undergoes adiabatic change from state $\left( {{P_1},\,{V_1},\,{T_1}} \right)$ to state $\left( {{P_2},\,{V_2},\,{T_2}} \right),$ then work done is $W = \frac{{\mu R\left( {{T_2} - {T_1}} \right)}}{{1 - \gamma }},$ where $\gamma = = \frac{{{C_p}}}{{{C_v}}}$ and R = universal gas constant.
Statement-II: In the above case, when work is done on the gas, the temperature of the gas would rise.
Choose the correct answer from the options given below

Assertion: Temperature is constant in a Quasi-static isothermal process.
Reason: No heat is exchanged with surrounding in a quasi-static isothermal process.

An ideal gas is allowed to expand freely against a vacuum in a rigid insulated container. The gas undergoes

A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2$R$, then the ratio of initial to final pressure is nearly equal to

An ideal gas is heated at constant pressure and absorbs amount of heat $Q$. If the adiabatic exponent is$\mathrm{\gamma }$, then the fraction of heat absorbed in raising the internal energy and performing the work, in

A monoatomic gas $(\gamma=5 / 3)$ at pressure $P$ is suddenly compressed to $1 / 64$ th of its volume adiabatically. Then, pressure of gas is:

In a heat engine, the temperature of the source and sink are $500 \mathrm{~K}$ and $375 \mathrm{~K}$. If the engine consumes $5 \times 10^5 \mathrm{~J}$ per cycle, the work done per cycle is:

By opening the door of a refrigerator inside a closed room, the room temperature

A total of $48 \mathrm{~J}$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^{\circ} \mathrm{C}$. The work done by the gas is : (Given, $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.)

In a given process on an ideal gas, $dW = 0$ and $\mathrm{dQ}<0$. Then for the gas

Assertion: Adiabatic free expansion is not a reversible process.
Reason: In adiabatic expansion internal does not change.

In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases $30joules$ of heat and 10 joules of work was done on the gas. If the initial internal energy of the gas was $30joules$ , then the final internal energy will be

Assertion (A): Straight line on $p-T$ graph for an ideal gas passing through origin represents isochoric process.

Reason (R): If $p \propto T, V=$ constant.

The change in internal energy of a given mass of gas, when its volume changes from$V$ to 2$V$ at constant pressure $p$ is $(\frac{{{C_p}}}{{{C_v}}} = \gamma$ universal gas constant=R)

One mole of ${\mathrm{O}_2}$ gas having a volume equal to $22.4litres$ at ${0^ \circ }C$ and 1 atmospheric pressure in compressed isothermally so that its volume reduces to $11.2litres$. The work done in this process is

An electric heater supplies heat to a gaseous system at a rate of 100 W. If system performs work at a rate of 80 joules per second, then what is the rate at which internal energy increases?