Concept Questions :-

Basic terms

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NEET - 2008

At ${10}^{\xb0}C$ the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At ${110}^{\xb0}C$ this ratio is

(a) x

(b)$\frac{383}{283}x$

(c)$\frac{10}{110}x$

(d) $\frac{283}{383}x$

Concept Questions :-

Basic terms

Writing ideal gas law

$PV=nRT\phantom{\rule{0ex}{0ex}}orPV=\frac{m}{M}RT\phantom{\rule{0ex}{0ex}}or\frac{PV}{m}=\frac{1}{M}RT\phantom{\rule{0ex}{0ex}}or\frac{P}{\rho}=\frac{RT}{M}\phantom{\rule{0ex}{0ex}}or\frac{\rho}{P}=\frac{1}{T}\phantom{\rule{0ex}{0ex}}\therefore \frac{{\rho}_{1}/{P}_{2}}{{\rho}_{2}/{P}_{1}}=\frac{{T}_{2}}{{T}_{1}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{\left({\rho}_{1}/{P}_{2}\right)}=\frac{383}{283}\phantom{\rule{0ex}{0ex}}or\frac{{\rho}_{2}}{{P}_{2}}=\frac{283}{383}x$

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Which of the following is not thermodynamical function ?

(1) Enthalpy

(2) Work done

(3) Gibb's energy

(4) Internal energy

Concept Questions :-

Basic terms

(2) Work done is not a thermodynamical function.

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Which of the following is not a thermodynamics co-ordinate ?

(1) *P*

(2) *T*

(3) *V*

(4) *R*

Concept Questions :-

Basic terms

(4) *R* is the universal gas constant.

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Which of the following statements is correct for any thermodynamic system ?

(1) The internal energy changes in all processes

(2) Internal energy and entropy are state functions

(3) The change in entropy can never be zero

(4) The work done in an adiabatic process is always zero

Concept Questions :-

Basic terms

(2) The internal energy and entropy depend only on the initial and final states of the system and not on the path followed to attain that state.

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A monoatomic gas of *n*-moles is heated from temperature *T*_{1} to *T*_{2} under two different conditions (i) at constant volume and (ii) at constant pressure. The change in internal energy of the gas is

(1) More for (i)

(2) More for (ii)

(3) Same in both cases

(4) Independent of number of moles

Concept Questions :-

Basic terms

(3) Change in internal energy $\Delta U=\mu {C}_{V}\Delta T$

it doesn’t depend upon type of process. Actually it is a state function

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In an isothermal change, an ideal gas obeys -

(1) Boyle's law

(2) Charle's law

(3) Gaylussac law

(4) None of the above

Concept Questions :-

Basic terms

(1) In isothermal process, compressibility *E _{θ}* =

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A gas mixture consists of 2 moles of oxygen and 4 moles argon at temperature *T*. Neglecting all vibrational modes, the total internal energy of the system is

(1) 4 *RT*

(2) 15 *RT *

(3) 9 *RT*

(4) 11 *RT *

Concept Questions :-

Basic terms

(4) Oxygen is diatomic gas, hence its energy of two moles $=2\times \frac{5}{2}RT=5RT$

Argon is a monoatomic gas, hence its internal energy of 4 moles $=4\times \frac{3}{2}RT=6RT$

Total Internal energy = (6 + 5)*RT* = 11*RT*

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Which one of the following gases possesses the largest internal energy** ?**

(1) 2 moles of helium occupying 1*m*^{3 }at 300 *K*

(2) 56 *kg* of nitrogen at *Nm*^{–2} and 300 *K*

(3) 8 grams of oxygen at 8 atm and 300 *K*

(4) 6 × 10^{26} molecules of argon occupying 40 *m*^{3} at 900 *K*

Concept Questions :-

Basic terms

(2) $\Delta U=\mu \text{}{C}_{V}\Delta T=\frac{m}{M}{C}_{V}\Delta T=\frac{N}{{N}_{A}}{C}_{V}\Delta T$

⇒ ${\left(\Delta U\right)}_{N}=\frac{56\times {10}^{3}}{28}\times \frac{5}{2}R\times 300$

and ${\left(\Delta U\right)}_{Ar}=\frac{6\times {10}^{26}}{6\times {10}^{23}}\times \frac{3}{2}R\times 900\Rightarrow {\left(\Delta U\right)}_{Ar}>{\left(\Delta U\right)}_{N}$

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A system goes from *A* to *B* via two processes I and II as shown in figure. If Δ*U*_{I} and Δ*U*_{II} are the changes in internal energies in the processes I and II respectively, then

(1) Δ*U*_{II} > Δ*U*_{I}

(2) Δ*U*_{II} < Δ*U*_{I}

(3) Δ*U*_{I} = Δ*U*_{II}

(4) Relation between Δ*U*_{I} and Δ*U*_{II} can not be determined

Concept Questions :-

Basic terms

(3) As internal energy is a state function therefore change in internal energy does not depends upon the path followed i.e. $\Delta {U}_{\text{I}}=\Delta {U}_{\text{II}}$

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