Carnot engine, having an efficiency of $\eta = 1/10$. As heat engine, is used as a refrigerator. If the work done on the system is $10\text{ J}$, the amount of energy absorbed from the reservoir at lower temperature is: (2015)
Using $\beta = \frac{1-\eta}{\eta} = 9$, the heat absorbed at lower temperature is $Q_2 = \beta W = 9 \times 10\text{ J} = 90\text{ J}$.
The efficiency of Carnot engine is $50\%$ and temperature of sink is $500\text{ K}$. If temperature of source is kept constant and its efficiency raised to $60\%$, then the required temperature of the sink will be: (2007)
Source temperature $T_1 = \frac{T_2}{1-\eta_1} = \frac{500}{0.5} = 1000\text{ K}$. New sink temperature $T_2' = T_1(1-\eta_2) = 1000(1 - 0.6) = 400\text{ K}$.
The equation of state for $5 \text{ g}$ of oxygen at a pressure $P$ and temperature $T$, when occupying a volume $V$, will be: (2004)
The number of moles $n = \frac{\text{given mass}}{\text{molar mass}}$. For $5 \text{ g}$ of $O_2$ gas, $n = \frac{5}{32}$. Substituting this into the ideal gas equation $PV = nRT$, we get $PV = (\frac{5}{32})RT$.
The value of critical temperature in terms of Van der Waals’ constant $a$ and $b$ is given by: (1996)
The critical temperature $T_c$ for a real gas obeying the Van der Waals equation is theoretically derived as $T_c = \frac{8a}{27Rb}$, where $a$ and $b$ are the Van der Waals constants.
According to kinetic theory of gases, at absolute zero temperature (1990)
Kinetic energy is directly proportional to the absolute temperature ($E_k = \frac{3}{2}kT$). At absolute zero ($T = 0 \text{ K}$), the translational kinetic energy becomes zero, implying that all molecular motion stops.
At constant volume temperature is increased then: (1989)
An increase in temperature raises the thermal agitation (root-mean-square speed) of gas molecules. This causes them to travel faster, increasing the frequency of their collisions with the container walls.
The volume occupied by the molecules contained in $4.5 \text{ kg}$ water at STP, if the intermolecular forces vanish away is: (2022)
At STP, 1 mole of an ideal gas occupies $22.4 \text{ L}$. The number of moles in $4.5 \text{ kg}$ of water is $n = \frac{4500 \text{ g}}{18 \text{ g/mol}} = 250 \text{ moles}$. The volume is $V = 250 \times 22.4 \text{ L} = 5600 \text{ L} = 5.6 \text{ m}^3$.
A cylinder contains hydrogen gas at pressure of $249 \text{ kPa}$ and temperature $27^\circ\text{C}$. Its density is : ($R = 8.3 \text{ J mol}^{-1} \text{ K}^{-1}$) (2020)
Using the ideal gas law in terms of density, $P = \frac{\rho RT}{M}$, we get $\rho = \frac{PM}{RT}$. For hydrogen, $M = 2 \times 10^{-3} \text{ kg/mol}$. Thus, $\rho = \frac{249 \times 10^3 \times 2 \times 10^{-3}}{8.3 \times 300} = 0.2 \text{ kg/m}^3$.
An ideal gas equation can be written as $P = \frac{\rho RT}{M_0}$ where $\rho$ and $M_0$ are respectively, (2020-Covid)
In the equation $P = \frac{\rho RT}{M_0}$, $\rho$ represents the mass density (mass per unit volume) of the gas, and $M_0$ is the molar mass of the gas.
Increase in temperature of a gas filled in a container would lead to: (2019)
According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to its absolute temperature ($E_k \propto T$). Therefore, an increase in temperature increases its kinetic energy.