Question:
Match the following:
Match the following:
Show Hint
Remember the key thermodynamic conditions:
Isothermal \(\rightarrow\) constant temperature
Adiabatic \(\rightarrow q=0\)
Isobaric \(\rightarrow\) constant pressure
Isochoric \(\rightarrow \Delta V=0\)
Isothermal \(\rightarrow\) constant temperature
Adiabatic \(\rightarrow q=0\)
Isobaric \(\rightarrow\) constant pressure
Isochoric \(\rightarrow \Delta V=0\)
Updated On: Jun 22, 2026
- \(A-(iv),\; B-(iii),\; C-(ii),\; D-(i)\)
- \(A-(iii),\; B-(iv),\; C-(i),\; D-(ii)\)
- \(A-(i),\; B-(ii),\; C-(iii),\; D-(iv)\)
- \(A-(ii),\; B-(i),\; C-(iv),\; D-(iii)\)
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The Correct Option is A
Solution and Explanation
Step 1: Match the Isothermal process.
In an isothermal process, temperature remains constant.
For an ideal gas, internal energy depends only on temperature. Therefore:
\[ \Delta U = 0 \] The work done in an isothermal reversible expansion or compression is given by:
\[ W=-nRT\ln\left(\frac{V_f}{V_i}\right) \] Thus,
\[ A \rightarrow (iv) \]
Step 2: Match the Adiabatic process.
In an adiabatic process, there is no heat exchange between the system and surroundings.
Hence,
\[ q=0 \] From the first law of thermodynamics:
\[ \Delta U = q + W \] Since \(q=0\),
\[ \Delta U = W \] Thus,
\[ B \rightarrow (iii) \]
Step 3: Match the Isobaric process.
In an isobaric process, pressure remains constant.
The work done at constant pressure is:
\[ W=-P\Delta V \] Hence,
\[ C \rightarrow (ii) \]
Step 4: Match the Isochoric process.
In an isochoric process, volume remains constant.
Therefore,
\[ \Delta V =0 \] and no work is done:
\[ W=0 \] Using the first law of thermodynamics:
\[ \Delta U = q + W \] Since \(W=0\),
\[ q=\Delta U \] Thus,
\[ D \rightarrow (i) \]
Step 5: Write the complete matching.
\[ A-(iv) \] \[ B-(iii) \] \[ C-(ii) \] \[ D-(i) \] This corresponds to option (1).
Step 6: Final conclusion.
Hence, the correct matching is:
\[ \boxed{A-(iv),\; B-(iii),\; C-(ii),\; D-(i)} \]
In an isothermal process, temperature remains constant.
For an ideal gas, internal energy depends only on temperature. Therefore:
\[ \Delta U = 0 \] The work done in an isothermal reversible expansion or compression is given by:
\[ W=-nRT\ln\left(\frac{V_f}{V_i}\right) \] Thus,
\[ A \rightarrow (iv) \]
Step 2: Match the Adiabatic process.
In an adiabatic process, there is no heat exchange between the system and surroundings.
Hence,
\[ q=0 \] From the first law of thermodynamics:
\[ \Delta U = q + W \] Since \(q=0\),
\[ \Delta U = W \] Thus,
\[ B \rightarrow (iii) \]
Step 3: Match the Isobaric process.
In an isobaric process, pressure remains constant.
The work done at constant pressure is:
\[ W=-P\Delta V \] Hence,
\[ C \rightarrow (ii) \]
Step 4: Match the Isochoric process.
In an isochoric process, volume remains constant.
Therefore,
\[ \Delta V =0 \] and no work is done:
\[ W=0 \] Using the first law of thermodynamics:
\[ \Delta U = q + W \] Since \(W=0\),
\[ q=\Delta U \] Thus,
\[ D \rightarrow (i) \]
Step 5: Write the complete matching.
\[ A-(iv) \] \[ B-(iii) \] \[ C-(ii) \] \[ D-(i) \] This corresponds to option (1).
Step 6: Final conclusion.
Hence, the correct matching is:
\[ \boxed{A-(iv),\; B-(iii),\; C-(ii),\; D-(i)} \]
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