What is the work done in $erg$ for the reversible expansion of $1 \, \text{mole}$ of an ideal gas from $10 \, L$ to $20 \, L$ at $25 \, ^oC$?
- A$-2.303 \times 8.314 \times 10^7 \times 298 \log(2)$
- B$-2.303 \times 8.314 \times 298 \log(2)$
- C$2.303 \times 8.314 \times 10^7 \times 298 \log(0.5)$
- D$2.303 \times 8.314 \times 298 \log(2)$
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An ideal gas undergoes a reversible isothermal expansion from state $I$ to state $II$ followed by a reversible adiabatic expansion from state $II$ to state $III$. The correct plot$(s)$ representing the changes from state $I$ to state $III$ is(are)
($p$ : pressure,$V$ : volume,$T$ : temperature,$H$ : enthalpy,$S$ : entropy)
($p$ : pressure,$V$ : volume,$T$ : temperature,$H$ : enthalpy,$S$ : entropy)
Match List-$I$ with List-$II$.
List-$I$ $(\text{Partial Derivatives})$ List-$II$ $(\text{Thermodynamic Quantity})$ $(A). \left(\frac{\partial G}{\partial T}\right)_{P}$ $(I). C_P$ $(B). \left(\frac{\partial H}{\partial T}\right)_{P}$ $(II). -S$ $(C). \left(\frac{\partial G}{\partial P}\right)_{T}$ $(III). C_V$ $(D). \left(\frac{\partial U}{\partial T}\right)_{V}$ $(IV). V$
Choose the correct answer from the options given below:
| List-$I$ $(\text{Partial Derivatives})$ | List-$II$ $(\text{Thermodynamic Quantity})$ |
| $(A). \left(\frac{\partial G}{\partial T}\right)_{P}$ | $(I). C_P$ |
| $(B). \left(\frac{\partial H}{\partial T}\right)_{P}$ | $(II). -S$ |
| $(C). \left(\frac{\partial G}{\partial P}\right)_{T}$ | $(III). C_V$ |
| $(D). \left(\frac{\partial U}{\partial T}\right)_{V}$ | $(IV). V$ |
DifficultJEE MAIN 2025
View SolutionFor the combustion of one mole of acetic acid,the work done at $298 \ K$ is (in $J$)
DifficultMHT CET 2022
View SolutionFind the enthalpy of neutralisation in $kJ/mol$ for the reaction between $NH_4OH$ and $HCN$ in aqueous solution,given that the enthalpies of ionisation of $NH_4OH$ and $HCN$ are $7 \ kJ/mol$ and $8 \ kJ/mol$ respectively,and the enthalpy of neutralisation of a strong acid and a strong base is $-57.3 \ kJ/mol$.
Medium
View SolutionMatch the following terms in Column-$I$ with their corresponding descriptions in Column-$II$:
Column-$I$ Column-$II$ $(a)$ Adiabatic process $(1)$ Heat $(b)$ Isolated system $(2)$ At constant volume $(c)$ Isothermal change $(3)$ First law of thermodynamics $(d)$ Path function $(4)$ No exchange of matter and energy $(e)$ State function $(5)$ No heat exchange $(f)$ $\Delta U = q$ $(6)$ Constant temperature $(g)$ Law of conservation of energy $(7)$ Internal energy $(h)$ Reversible process $(8)$ $p_{ext} = 0$ $(i)$ Free expansion $(9)$ At constant pressure $(j)$ $\Delta H = q$ $(10)$ Infinitely slow process involving multiple equilibrium states $(k)$ Intensive property $(11)$ Entropy $(l)$ Extensive property $(12)$ Pressure,$(13)$ Specific heat
| Column-$I$ | Column-$II$ |
| $(a)$ Adiabatic process | $(1)$ Heat |
| $(b)$ Isolated system | $(2)$ At constant volume |
| $(c)$ Isothermal change | $(3)$ First law of thermodynamics |
| $(d)$ Path function | $(4)$ No exchange of matter and energy |
| $(e)$ State function | $(5)$ No heat exchange |
| $(f)$ $\Delta U = q$ | $(6)$ Constant temperature |
| $(g)$ Law of conservation of energy | $(7)$ Internal energy |
| $(h)$ Reversible process | $(8)$ $p_{ext} = 0$ |
| $(i)$ Free expansion | $(9)$ At constant pressure |
| $(j)$ $\Delta H = q$ | $(10)$ Infinitely slow process involving multiple equilibrium states |
| $(k)$ Intensive property | $(11)$ Entropy |
| $(l)$ Extensive property | $(12)$ Pressure,$(13)$ Specific heat |
Medium
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