A. Zeroth law of thermodynamics gives concept of temperature
B. First law of thermodynamics gives concept of internal energy
C. In isothermal expansion of ideal gas, $\Delta Q \neq \Delta W$
D. Product of intensive and extensive variables is extensive
E. The ratio of any extensive variable to mass will be an extensive variable
Choose the correct combination of statements from the options given below:
Analyzing Thermodynamics Statements
We need to evaluate the correctness of the given statements regarding thermodynamics and variables.
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Statement A: Zeroth law of thermodynamics gives the concept of temperature.
The Zeroth Law states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This establishes the concept of temperature as a property that determines thermal equilibrium.
Result: Correct.
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Statement B: First law of thermodynamics gives the concept of internal energy.
The First Law is a statement of conservation of energy, often expressed as $\Delta U = \Delta Q - \Delta W$, where $\Delta U$ is the change in internal energy, $\Delta Q$ is heat added, and $\Delta W$ is work done by the system. It inherently defines and relates internal energy.
Result: Correct.
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Statement C: In isothermal expansion of ideal gas, $\Delta Q \neq \Delta W$.
For an ideal gas, internal energy ($U$) depends only on temperature ($T$). In an isothermal process, $\Delta T = 0$, which implies $\Delta U = 0$. According to the First Law ($\Delta U = \Delta Q - \Delta W$), if $\Delta U = 0$, then $\Delta Q = \Delta W$. The statement claims $\Delta Q \neq \Delta W$.
Result: Incorrect.
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Statement D: Product of intensive and extensive variables is extensive.
An intensive variable does not depend on the system size (e.g., temperature $T$, pressure $P$), while an extensive variable does (e.g., volume $V$, mass $m$). The product of an intensive variable and an extensive variable results in an extensive variable. For example, Pressure (intensive) $\times$ Volume (extensive) = Work (extensive).
Result: Correct.
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Statement E: The ratio of any extensive variable to mass will be an extensive variable.
Dividing an extensive variable by mass (which is also extensive) yields a specific property, which is intensive. For example, Volume (extensive) / Mass (extensive) = Specific Volume (intensive). Similarly, Energy (extensive) / Mass (extensive) = Specific Energy (intensive).
Result: Incorrect.
Identifying the Correct Combination
Based on the analysis, statements A, B, and D are correct. Statement C claims $\Delta Q \neq \Delta W$ in isothermal expansion of an ideal gas, which is false ($\Delta Q = \Delta W$); Statement E claims the ratio of extensive/mass is extensive, which is false (it's intensive).
Therefore, the correct combination includes statements A, B, and D.
Similar Questions
- Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is $32 \times 10^{18}$ /s then collision frequency in gas A is _________ /s.
- An insulated cylinder of volume $60 \text{ cm}^3$ is filled with a gas at $27^\circ\text{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 \text{ cm}^3$ while allowing the temperature to rise to $77^\circ\text{C}$. The final pressure is _________ atmospheric pressure.
- A brass wire of length 2 m and radius 1 mm at $27^\circ\text{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^\circ\text{C}$ creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4T$, is ______ $^\circ\text{C}$.
- A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^\circ\text{C}$. The gas is now heated to double its temperature. The modified pressure is ______ Pa.
10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_1$ to $P_2$ is $\alpha \text{ Joule}$ ($P_1 = 21.7 \text{ Pa}$ and $P_2 = 30 \text{ Pa}, C_v = 21 \text{ J/K.mol}, R = 8.3 \text{ J/mol.K}$). The value of $\alpha$ is _______.
- When $300 \text{ J}$ of heat given to an ideal gas with $C_p = \frac{7}{2} R$ its temperature raises from $20^\circ\text{C}$ to $50^\circ\text{C}$ keeping its volume constant. The mass of the gas is (approximately) _______ g. ($R = 8.314 \text{ J/mol.K}$)
- The mean free path of a molecule of diameter $5 \times 10^{-10}\text{ m}$ at the temperature $41^{\circ}\text{C}$ and pressure $1.38 \times 10^{5}\text{ Pa}$, is given as _________ $\text{m}$. (Given $k_{\text{B}} = 1.38 \times 10^{-23}\text{ J/K}$).
A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle $ABC$ is _________ $\text{J}$.
- A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\text{rd}}$ of its initial volume ($V_o = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5 \text{ N/m}^2$, the magnitude of work done on the gas is _________ J.
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = n C_v (T_f - T_i) = \frac{nR}{\gamma - 1}(T_f - T_i)$, where $\gamma = \frac{C_p}{C_v}$, $T_i = \text{initial temperature}$, $T_f = \text{final temperature}$.
Statement II: Relation between degree of freedom $f$ and $\gamma (= C_p / C_v)$ is $\left(\gamma = 1 + \frac{2}{f}\right)$
Choose the correct answer from the options given below
Important Questions from Heat and Thermodynamics
- Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is $32 \times 10^{18}$ /s then collision frequency in gas A is _________ /s.
- An insulated cylinder of volume $60 \text{ cm}^3$ is filled with a gas at $27^\circ\text{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 \text{ cm}^3$ while allowing the temperature to rise to $77^\circ\text{C}$. The final pressure is _________ atmospheric pressure.
- A brass wire of length 2 m and radius 1 mm at $27^\circ\text{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^\circ\text{C}$ creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4T$, is ______ $^\circ\text{C}$.
- A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^\circ\text{C}$. The gas is now heated to double its temperature. The modified pressure is ______ Pa.
10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_1$ to $P_2$ is $\alpha \text{ Joule}$ ($P_1 = 21.7 \text{ Pa}$ and $P_2 = 30 \text{ Pa}, C_v = 21 \text{ J/K.mol}, R = 8.3 \text{ J/mol.K}$). The value of $\alpha$ is _______.
