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A system is given $300$ calories of heat and it does $600$ joules of work. How much does the internal energy of the system change in this process? $( J =4.18$ $Joules / cal )$ (in joule)
An ideal gas with constant heat capacity $C_V=\frac{3}{2} n R$ is made to carry out a cycle that is depicted by a triangle in the figure given below. The following statement is true about the cycle.
Consider $1 \,kg$ of liquid water undergoing change in phase to water vapour at $100^{\circ} C$. At $100^{\circ} C$, the vapour pressure is $1.01 \times 10^5 \,N - m ^2$ and the latent heat of vaporization is $22.6 \times 10^5 \,Jkg ^{-1}$. The density of liquid water is $10^3 \,kg m ^{-3}$ and that of vapour is $\frac{1}{1.8} \,kg m ^{-3}$. The change in internal energy in this phase change is nearly ............ $\,J kg ^{-1}$
Three moles of an ideal gas $\left( {{C_P} = \frac{7}{2}R} \right)$ at pressure ${P_A}$ and temperature ${T_A}0$ is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally the gas is compressed at constant volume to its original pressure ${P_A}.$ The correct $P-V$ and $P-T$ diagrams indicating the process are
A reversible engine has an efficiency of $\frac{1}{4}$. If the temperature of the sink is reduced by $58^{\circ} {C}$, its efficiency becomes double. Calculate the temperature of the sink. (In $^{\circ} {C}$)
Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, $\mathrm{T}_{1}$ and $\mathrm{T}_{2} .$ The temperature of the hot reservoir of the first engine is $\mathrm{T}_{1}$ and the temperature of the cold reservoir of the second engine is $\mathrm{T}_{2} . T$ is temperature of the sink of first engine which is also the source for the second engine. How is $T$ related to $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$, if both the engines perform equal amount of work?