Relation between Cp and Cv

Q. The value of $\gamma$ on monoatomic, diatomic and triatomic gases is ___, ___ and ___ respectively.

1. 1.33, 1.40, 1.66

2. 1.66, 1.40, 1.33

3. None of these

4. 2, 1.66, 1.5

Q. During nitrogen estimation of an organic compound by Kjeldahl's method, the ammonia evolved by 0.5 g of the compound neutralised 10 ml of 1 M $H_{2}S{O}_4$. Calculate the percentage of nitogen in the compound.

1. 50 %
2. 60 %
3. 56 %
4. 66 %

Q. Which one among the following is the correct option for right relationship between $C_{P}and{C}_V$ for one mole of ideal gas?

1. $C_P+C_V=R$

2. $C_P-C_V=R$
3. $C_P={RC}_V$

4. $C_V=R{C}_P$

Q.

The efficiency of the Carnot engine working between the ice point and the steam point would be

Q.

For the reaction $\mathrm{A}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{B}\left(\mathrm{g}\right)$ at $495\mathrm{K}$ ;:${\mathrm{\Delta rG}}_{\mathrm{o}}=–9.478\mathrm{kJ}{\mathrm{mol}}^{-1}$

If we start the reaction in a closed container at $495\mathrm{K}$ with $22$millimoles of $\mathrm{A}$, the amount of $\mathrm{B}$ in the equilibrium mixture is ________millimoles. (Round off to the nearest Integer).

[$\mathrm{R}=8.314{\mathrm{Jmol}}^{-1}{\mathrm{K}}^{-1};\ln 10=2.303$]

Q.

Consider the following statements : For diatomic gases, the ratio $\frac{C_p}{C_v}$ is equal to

(1) 1.40 (lower temperature)

(2) 1.66 (moderate temperature)

(3) 1.29 (higher temperature) Which of the above statements are correct

1. 1, 2 and 3

2. 1 and 2

3. 2 and 3

4. 1 and 3

Q. To raise the temperature of 1 mole of a diatomic gas by $1{}^{\circ }C$ at constant pressure, the required amount of heat is $120cal.$
The amount of heat which goes as the internal energy is almost equal to:

1. $85.7cal$
2. $58.8cal$
3. $82.5cal$
4. $80.2cal$

Q. 1 mole of an ideal gas expands isothermally reversibly from 2 litre to 4 litre and 3 moles of the same gas expands from 2 litre to x litre and doing same work, what is 'x'?

1. ${\left(8\right)}^{1/3}$

2. ${\left(4\right)}^{2/3}$

3. 2
4. 4

Q. What is the relation between $C_p$ and $C_v$ ?

Q.

$70$Cal heat is required to raise the temperature of $2$ moles of an Ideal gas at constant pressure from $25°\mathrm{C}$ to $30°\mathrm{C}$, then the amount of heat, required to raise the temperature of the same gas through the same rise of temp, at constant volume is

Q.

Cp and Cv are specific heats at constant pressure and constant volume, respectively. It is observed that Cp − Cv =a for hydrogen gas Cp − Cv =b for nitrogen gas. The correct relation between a and b is :

Q. Consider a closed system (cylinder) whose walls are adiabatic. The cylinder lies in a horizontal position & is divided into three parts $A_1$, $A_2$ and $A_3$ by means of partions $S_1$ and $S_2$ which can move along the length of the cylinder without friction, $S_1$ is adiabatic while $S_2$ is conducting. Initially each of the parts $A_1$, $A_2$ & $A_3$ contains one mole of He gas at pressure $P_0$, temperature $T_0$ & volume $V_0$.
($C_v=\frac{3}{2}R,C_p=\frac{5}{2}R,\gamma =\frac{5}{3}$, take He as an ideal mono atomic gas)
Now heat is supplied slowly to the gas in part $A_1$, till the Temperature in part $A_3$ becomes $$T_3=\frac{9T_0}{4}$$.
Which statement(s) is/are correct?

1. $P_1$=$P_2$=$P_3$
2. $V_1$>$V_2$=$V_3$
3. $T_1$>$T_2$>$T_3$
4. $V_1=\frac{65}{27}{V}_0$

Q.

In an isobaric process, the ratio of heat supplied to the system (dQ) and work done by the system (dW) for diatomic gas is

1. 7 : 2

2. 7 : 5

3. 5 : 7

4. 1 : 1

Q. For hydrogen gas, $C_p-C_v$ = a and for nitrogen gas $C_p-C_v$ = b, then the relation between a and b is:
(where $C_p$ and $C_v$ are specific heats defined per gram)

1. $a=16b$
2. $a=14b$
3. $b=16a$
4. $a=b$

Q. $C_P-C_V$ for an ideal gas is R. Explain.

Q. 18. Assertion :Cp - Cv = R Reason : R is work done when temperature of one mole of ideal gas is increased by 1^°

Q. The thermal dissociation equilibrium of $CaC{O}_3\left(s\right)$ is studied under different conditions
$CaC{O}_3\left(s\right)\rightleftharpoons CaO\left(s\right)+C{O}_2\left(g\right)$
For this equilibrium, the correct statement(s) is/are :

1. $\Delta H$ is dependent on $T$
2. $K$ is independent of the initial amount of $CaC{O}_3$
3. $K$ is dependent on the pressure of $C{O}_2$, at a given $T$
4. $\Delta H$ is independent of catalyst, if any

Q. 28. One mole of an ideal gas undergoes process in which P is directly proportional to 1/T, then molar heat capacity of gas is.

Q. pressure of 1g of ideal gas A at 300K is 1 bar.when 2g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar.Find relatin between their molecular masses.

Q. For $2$ mole of an ideal gas; the relation between $C_p$ & $C_v$ (non-molar) are :

1. $C_p-C_v=2R$
2. $C_v-C_p=2R$
3. $C_p-C_v=R$
4. $C_v-C_p=R$

Q. In an isobaric process, the ratio of heat supplied to the system (dq) and work done by the system (dW) for diatomic gas is:

1. $5:7$
2. $1:1$
3. $7:5$
4. $7:2$

Q. The enthalpy of hydrogenation of cyclohexene is $-119.5\text{kJ/ mol}$. If resonance energy of benzene is $-150.4\text{kJ/mol}$ then what is its enthalpy of hydrogenation?

1. $-259.9\text{kJ/mol}$
2. $-358.5\text{kJ/mol}$
3. $-508.9\text{kJ/mol}$
4. $-208.1\text{kJ/mol}$

Q. A $0.60$ g nitrogen containing compound was boiled with $NaOH$, and $N{H}_3$ thus formed, required $100$ mL of $0.2$ N $H_{2}S{O}_4$ for neutralisation. The percentage of nitrogen in the compound is:

1. $46.67\%$
2. $60.00\%$
3. $20.00\%$
4. $23.34\%$

Q.

When to use which value of gas constant

Q. The thermal dissociation equilibrium of $CaC{O}_3\left(s\right)$ is studied under different conditions.
$CaC{O}_3\left(s\right)\rightleftharpoons CaO\left(s\right)+C{O}_2\left(g\right)$
For this equilibrium, the correct statement(s) is (are) :

1. $\Delta H$ is dependent on $T$
2. $K$ is independent of the initial amount of $CaC{O}_3$
3. $K$ is dependent on the pressure of $C{O}_2$ at a given $T$
4. $\Delta H$ is independent of the catalyst, if any

Q. When one mole of an ideal gas is compressed to half its initial volume and simultaneously heated to twice its initial temperature, the change in entropy $\left(△S\right)$ is :

1. $C_{P}ln2$
2. $Rln2$
3. $(C_V-R)ln2$
4. $C_{V}ln2$

Q. One litre of gas is at temperature 25^°C and pressure 10 to power minus 6.How many molecules are present in the vessel?

Q. $C_P-C_V$ for an ideal gas is $R$.
State whether the statement is True or False

Q. A gas $(C_{v,m}=\frac{5}{2}R)$ behaving ideally was allowed to expand reversibly and adiabatically from $1litre$ to $32litre$. It's initial temperature was ${327}^{o}C.$ The molar enthalpy change (in $Jmol{e}^{-1}$) for the process is

1. $-1125R$
2. $-575R$
3. $-1575R$
4. None of these

Q. A gaseous mixture of $He$ & $C{H}_4$ gases with mole ratio 2 : 1 respectively is placed in a container and allowed to effuse through a small orifice. $Xml$ of the $He$ gas effuses in 5 seconds. The time required to effuse same volume of $C{H}_4$ gas is:

1. 40 $sec$
2. 20 $sec$
3. 5 $sec$
4. 10 $sec$