A blackbody and a real body of identical dimensions are heated to same temperature. If ratio of rates of radiation of the blackbody and the real body is $4 : 3$, then emissivity of the real body is equal to
The rate of radiation is given by $E = e\sigma A T^4$. For a blackbody, $e = 1$. Given $\frac{E_b}{E} = \frac{4}{3} ⇒ \frac{1}{e} = \frac{4}{3}$, hence emissivity $e = 0.75$.
Water equivalent of a metallic bar is $100\text{ g}$, the energy required to increase its temperature by $1^\circ\text{C}$ is
Energy required is $Q = w \cdot \Delta T$, where $w$ is the water equivalent. Thus, $Q = 100\text{ g} \times 1\text{ cal/g}^\circ\text{C} \times 1^\circ\text{C} = 100\text{ cal}$.
For $n$ mole of an ideal gas, the correct equation of $1^{\text{st}}$ law of thermodynamics corresponding to isobaric process will be (symbols have their usual meanings)
By first law, $Q = \Delta U + W$. In an isobaric process, the work done is $W = P\Delta V = nR\Delta T$. Therefore, both expressions are correct.
Consider the following thermodynamic parameters:
(a) Heat
(b) Internal energy
(c) Work
Which of the given parameters are path functions?
Heat and work depend on the path taken between states, whereas internal energy is a state function. Therefore, (a) and (c) are path functions.
In ideal condition, the maximum efficiency that can be derived from a heat engine operating between $600\text{ K}$ reservoir and $200\text{ K}$ sink, is
Efficiency is given by $\eta = 1 - \frac{T_{\text{sink}}}{T_{\text{source}}}$. Substituting the given values: $\eta = 1 -\frac{200}{600} =\frac{2}{3} \approx 66.67%$.
Which of the following is not the correct assumption of kinetic theory of gases?
Kinetic theory assumes that gas molecules undergo continuous random motion and collide with each other as well as with the walls of the container.
The equation of state for \(14\text{ g}\) nitrogen gas at a pressure \(P\) and temperature \(T\), when occupying a volume \(V\) will be
The molecular mass of nitrogen gas \((\text{N}_2)\) is \(28\text{ g/mol}\). The number of moles is \(n = \frac{14}{28} = 0.5\). Thus, using \(PV = nRT\), we get \(PV = \frac{1}{2}RT\).
The unit of emissive power is
Emissive power is defined as the thermal energy emitted per unit area per unit time, so its unit is \(\text{J m}^{-2}\text{ s}^{-1}\) (or \(\text{W m}^{-2}\)).
Two rods one made of material A and other made of material B of same length and same cross-sectional area are joined together. If thermal conductivity of material A is \(K_1\) while that of material B is \(K_2\) and the free end of rod made of material A is maintained at \(T_1\) while that of the rod of material B is maintained at \(T_2\), then the temperature of junction is (Where \(T_1 > T_2\))
Under steady state, the rate of heat flow is the same through both rods: \(\frac{K_1 A(T_1 - T_j)}{L} = \frac{K_2 A(T_j - T_2)}{L}\). Solving for \(T_j\) gives \(T_j = \frac{K_1 T_1 + K_2 T_2}{K_1 + K_2}\).
Consider the following statements out of which one is labelled as assertion and other as reason.
Assertion: The internal energy of an ideal monoatomic gas enclosed in a container does not change when there is no change in temperature.
Reason: Internal energy of a gaseous system is path function.
Internal energy of an ideal gas depends only on its temperature, so the Assertion is true. However, internal energy is a state function, not a path function, so the Reason is false.