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Standard XII

Chemistry

Difference between Internal Energy and Enthalpy

An ideal gas ...

Question

An ideal gas is subjected to an isothermal expansion such that its volume changes from $V_{i}$ to $V_{f}$ and pressure from $P_{i}$ to $P_{f}$ . The work done by the gas is:

W = + n R T log \frac{V_{f}}{V_{i}}

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W = - n R T log \frac{V_{f}}{V_{i}}

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W = n R T ln \frac{P_{f}}{P_{i}}

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W = - n R T log \frac{P_{f}}{P_{i}}

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Solution

The correct option is D $W = n R T ln \frac{P_{f}}{P_{i}}$
Work done in expansion of gas
$W = - n R T ln \frac{V_{f}}{V_{i}} = - n R T ln \frac{P_{i}}{P_{f}}$

So, work done by the gas $= n R T ln \frac{P_{f}}{P_{i}}$

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Similar questions

Q. The graph given below shows the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from

(P_{i}, V_{i})

(P_{f}, V_{f})

. Compare the work done in the above case with that carried out against a constant external pressure

P_{f}

(i) Area

A B V_{f} V_{i}

represents total work done for a reversible isothermal expansion from

(P_{i}, V_{i})

(P_{f}, V_{f})

.
(ii) Area

C B V_{f} V_{i}

represents work done against a constant pressure

P_{f}

Q. The graph given below shows the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from

(P_{i}, V_{i})

(P_{f}, V_{f})

. Compare the work done in the above case with that carried out against a constant external pressure

P_{f}

(i) Area

A B V_{f} V_{i}

represents total work done for a reversible isothermal expansion from

(P_{i}, V_{i})

(P_{f}, V_{f})

.
(ii) Area

C B V_{f} V_{i}

represents work done against a constant pressure

P_{f}

The pressure-volume work for an ideal gas can be calculated by using the expression $W = \int_{V_{i}}^{V_{f}} p_{e x} d V$ . The work can also be calculated from the pV-plot by using the area under the curve within the specified limits. When an ideal gas is compressed (a) reversibly or (b) irreversibly from volume $V_{i} t o V_{f}$ . Choose the correct option.
(a) W (reversible) = W (irreversible)
(b) W (reversible) < W (irreversible)
(c) W (reversible) = W (irreversible)
(d) W (reversible) = W (irreversible) $+ p_{e x} . Δ V$

An ideal gas expands isothermally from a volume $V_{1}$ to $V_{2}$ to and then compressed to original volume $V_{1}$ adiabatically. Initial pressure is $P_{1}$ and final pressure is $P_{3}$ . The total work done is W. Then

Q. For an ideal gas with initial pressure and volume

P_{i}

and

V_{i}

respectively, a reversible isothermal expansion happens, when its volume becomes

V_{0}

. Then it is compressed to its original volume

V_{i}

by a reversible adiabatic process. If the final pressure is

P_{t}

then which of the following statements is true?

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An ideal gas is subjected to an isothermal expansion such that its volume changes from Vi to Vf and pressure from Pi to Pf. The work done by the gas is:

The correct option is D W=nRTlnPfPiWork done in expansion of gasW=−nRTlnVfVi=−nRTlnPiPfSo, work done by the gas =nRTlnPfPi

An ideal gas is subjected to an isothermal expansion such that its volume changes from $V_{i}$ to $V_{f}$ and pressure from $P_{i}$ to $P_{f}$ . The work done by the gas is:

The correct option is D $W = n R T ln \frac{P_{f}}{P_{i}}$
Work done in expansion of gas
$W = - n R T ln \frac{V_{f}}{V_{i}} = - n R T ln \frac{P_{i}}{P_{f}}$

So, work done by the gas $= n R T ln \frac{P_{f}}{P_{i}}$