In Column-$I$ processes and in Column-$II$ the first law of thermodynamics are given. Match them appropriately:
Column-$I$ Column-$II$ $(a)$ Adiabatic $(i)$ $\Delta Q = \Delta U$ $(b)$ Isothermal $(ii)$ $\Delta Q = \Delta W$ $(iii)$ $\Delta U = -\Delta W$
| Column-$I$ | Column-$II$ |
|---|---|
| $(a)$ Adiabatic | $(i)$ $\Delta Q = \Delta U$ |
| $(b)$ Isothermal | $(ii)$ $\Delta Q = \Delta W$ |
| $(iii)$ $\Delta U = -\Delta W$ |
(A) The first law of thermodynamics is given by $\Delta Q = \Delta U + \Delta W$.
$(a)$ For an adiabatic process,there is no heat exchange with the surroundings,so $\Delta Q = 0$. Substituting this into the first law: $0 = \Delta U + \Delta W$,which implies $\Delta U = -\Delta W$. Thus,$(a)$ matches $(iii)$.
$(b)$ For an isothermal process,the temperature remains constant,which implies the change in internal energy $\Delta U = 0$. Substituting this into the first law: $\Delta Q = 0 + \Delta W$,which implies $\Delta Q = \Delta W$. Thus,$(b)$ matches $(ii)$.
Therefore,the correct matching is $(a-iii), (b-ii)$.
$(a)$ For an adiabatic process,there is no heat exchange with the surroundings,so $\Delta Q = 0$. Substituting this into the first law: $0 = \Delta U + \Delta W$,which implies $\Delta U = -\Delta W$. Thus,$(a)$ matches $(iii)$.
$(b)$ For an isothermal process,the temperature remains constant,which implies the change in internal energy $\Delta U = 0$. Substituting this into the first law: $\Delta Q = 0 + \Delta W$,which implies $\Delta Q = \Delta W$. Thus,$(b)$ matches $(ii)$.
Therefore,the correct matching is $(a-iii), (b-ii)$.
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Similar Questions
$A$ reversible cyclic process for an ideal gas is shown below. Here,$P, V$,and $T$ are pressure,volume,and temperature,respectively. The thermodynamic parameters $q, w, H$,and $U$ are heat,work,enthalpy,and internal energy,respectively.
The correct option$(s)$ is (are):
$(A)$ $q_{AC} = \Delta U_{BC}$ and $W_{AB} = P_2(V_2 - V_1)$
$(B)$ $W_{BC} = P_2(V_2 - V_1)$ and $q_{BC} = H_{AC}$
$(C)$ $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{BC}$
$(D)$ $q_{BC} = \Delta H_{AC}$ and $\Delta H_{CA} > \Delta U_{CA}$
The correct option$(s)$ is (are):
$(A)$ $q_{AC} = \Delta U_{BC}$ and $W_{AB} = P_2(V_2 - V_1)$
$(B)$ $W_{BC} = P_2(V_2 - V_1)$ and $q_{BC} = H_{AC}$
$(C)$ $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{BC}$
$(D)$ $q_{BC} = \Delta H_{AC}$ and $\Delta H_{CA} > \Delta U_{CA}$
Two cylinders of equal size are filled with an equal amount of ideal diatomic gas at room temperature. Both cylinders are fitted with pistons. In cylinder $A$,the piston is free to move (isobaric process),while in cylinder $B$,the piston is fixed (isochoric process). When the same amount of heat is supplied to both cylinders,the temperature of the gas in cylinder $A$ rises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B$ (in $;K$)?
Difficult
View SolutionWhen $100 \ J$ of heat is supplied to a gas,the increase in the internal energy of the gas is $60 \ J$. Then the gas is/can
Column-$I$ shows graphs of thermodynamic processes, and column-$II$ contains information about various thermodynamic variables. Match column-$I$ with the information in column-$II$.
Column-$I$ Column-$II$ $(A)$ $PV$ vs $V$ (Isothermal expansion) $(P)$ $W$ > 0 $(B)$ $P$ vs $T$ (Isochoric heating) $(Q)$ $W$ < 0 $(C)$ $P$ vs $V$ (Isobaric expansion) $(R)$ $\Delta Q$ > 0 $(D)$ $V$ vs $T$ (Isobaric compression) $(S)$ $\Delta U$ > 0 $(T)$ $\Delta U$ < 0
| Column-$I$ | Column-$II$ |
| $(A)$ $PV$ vs $V$ (Isothermal expansion) | $(P)$ $W$ > 0 |
| $(B)$ $P$ vs $T$ (Isochoric heating) | $(Q)$ $W$ < 0 |
| $(C)$ $P$ vs $V$ (Isobaric expansion) | $(R)$ $\Delta Q$ > 0 |
| $(D)$ $V$ vs $T$ (Isobaric compression) | $(S)$ $\Delta U$ > 0 |
| $(T)$ $\Delta U$ < 0 |
Medium
View SolutionTwo cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 \,K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 \,K$, what is the rise in temperature of the gas in $B$ (in $\,K$)? (Given $\gamma = 5/3$)
DifficultAP EAMCET 2007
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