Relation between cp and cv is given by (where cp = Specific heat at constant pressure, cv = Specific heat at constant volume, $$\gamma = \frac{{{{\text{c}}_{\text{p}}}}}{{{{\text{c}}_{\text{v}}}}},$$ known as adiabatic index and R = Gas constant)

In a two-electron atomic system having orbital and spin angular momenta $${l_1}{l_2}$$ and $${s_1}{s_2}$$ respectively, the coupling strengths are defined as $${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}},\,{\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}},\,{\Gamma _{{l_1}{l_2}}}$$ and $${\Gamma _{{l_2}{s_1}}}.$$ For the jj coupling. scheme to be applicable, the coupling strengths must satisfy the condition

A

$${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}} > {\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}}$$

B

$${\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}} > {\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}}$$

C

$${\Gamma _{{l_1}{s_2}}},\,{\Gamma _{{l_2}{s_1}}} > {\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}}$$

D

$${\Gamma _{{l_1}{s_2}}},\,{\Gamma _{{l_2}{s_1}}} > {\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}}$$

Relation between cp and cv is given by (where cp = Specific heat at constant pressure, cv = Specific heat at constant volume, γ = cp/cv, known as adiabatic index, and R = Gas constant)

A

cv/ cp =R

B

cp - cv = R

C

cv = R/ γ-1

D

Both (B) and (C)

The resonance widths $$\Gamma $$ of $$\rho ,\,\omega $$ and $$\phi $$ particle resonances satisfy the relation $${\Gamma _\rho } > {\Gamma _\omega } > {\Gamma _\phi }$$ . Their lifetimes r satisfy the relation

A

$${\tau _\rho } > {\tau _\omega } > {\tau _\phi }$$

B

$${\tau _\rho }

C

$${\tau _\rho } {\tau _\phi }$$

D

$${\tau _\rho } > {\tau _\omega }

The heat supplied to the gas at constant volume is (where m = Mass of gas, C_v = Specific heat at constant volume, C_p = Specific heat at constant pressure, T₂ - T₁ = Rise in temperature and R = Gas constant)

A

mR (T₂ - T₁)

B

mC_v (T₂ - T₁)

C

mC_p (T₂ - T₁)

D

None of the above

Work-done during adiabatic expansion is given by (where p₁, v₁, T₁ = Pressure, volume and temperature for the initial condition of gas, p₂, v₂, T₂ = Corresponding values for the final condition of gas, R = Gas constant and $$\gamma $$ = Ratio of specific heats)

A

$$\frac{{{{\text{p}}_1}{{\text{v}}_1} - {{\text{p}}_2}{{\text{v}}_2}}}{{\gamma - 1}}$$

B

$$\frac{{{\text{mR}}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{\gamma - 1}}$$

C

$$\frac{{{\text{mR}}{{\text{T}}_1}}}{{\gamma - 1}}\left( {1 - \frac{{{{\text{p}}_2}{{\text{v}}_2}}}{{{{\text{p}}_1}{{\text{v}}_1}}}} \right)$$

D

All of these

Group I shows different heat addition processes in power cycles. Likewise, Group II shows different heat removal processes. Group III lists power cycles. Match items from Groups I, II and III. Group I Group II Group III P. Pressure constant S. Pressure constant 1. Rankine cycle Q. Volume constant T. Volume constant 2. Otto cycle R. Temperature constant U. Temperature constant 3. Carnot cycle 4. Diesel cycle 5. Brayton cycle

A

P – S – 5, R – U – 3, P – S – 1, Q – T - 2

B

P – S – 1, R – U – 3, P – S – 4, P – T - 2

C

R – T – 3, P – S – 1, P – T – 4, Q – S - 5

D

P – T – 4, R – S – 3, P – S – 1, P – S - 5

The molar specific heat constant pressure of an ideal gas is 7R/2. The ratio of specific heat at constant pressure to that at constant volume is?

A

9/7

B

8/7

C

7/5

D

5/7

Characteristic gas constant is given by (here cp=specific heat at constant pressure and cv is the specific heat at constant volume)

A

R=cv – cp

B

R=cp + cv

C

R=cp – cv

D

none of the mentioned

According to Regnault's law, the specific heat at constant pressure (cp) and specific heat at constant volume (cv) _________ with the change in pressure and temperature of the gas.

A

Change

B

Do not change

C

Both (A) and (B)

D

None of these

Alpha, Beta and Gama went for a picnic at Jurassic Park, when they feel hungry they took out the stuff they brought. Alpha bought 6 sandwiches while Beta bought 4 and Gamma bought none. Both Alpha and Beta shared their sandwiches with Gamma such that each got the same amount. If Gamma paid a total amount of Rs. 10 to Alpha and Beta, how much of Rs. 10 should Alpha get ? (Assume that sandwiches and rupees can be split.)

A

8

B

6

C

3

D

None of these

Relation between c_p and c_v is given by (where c_p = Specific heat at constant pressure, c_v = Specific heat at constant volume, $$\gamma = \frac{{{{\text{c}}_{\text{p}}}}}{{{{\text{c}}_{\text{v}}}}},$$ known as adiabatic index and R = Gas constant)

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