Thermodynamics Test

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Thermodynamics Test - 77

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Weekly Quiz Competition

Question 1
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A gas mixture consists of $$2$$ moles of O, and $$4$$ moles of Ar at a temperature T. Neglecting all vibrational moles, the total internal energy of the system is

A
$$4RT $$

B
$$15RT $$

C
$$9RT$$

D
$$11RT$$

Solution
Question 2
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Hess's law states that:

A
The standard enthalpy of an overall reaction is the sum of the enthalpy changes in individual reactions.

B
Enthalpy of formation of a compound is same as the enthalpy of decomposition of the compound into constituent elements, but with opposite sign.

C
At constant temperature, the pressure of a gas is inversely proportional to its volume

D
The mass of a gas dissolve per liter of a solvent is proportional to the pressure of the gas in equilibrium with the solution.

Solution
Question 3
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Consider $$Zn+Cu^{2+}\rightarrow Zn^{2+}+Cu$$ If the standard emf is $$E_{cell}^o=2.0V$$ and $$F=96500C$$
Find $$\Delta G^0$$(kJmol)

A
$$-388$$

B
$$+388$$

C
$$-194$$

D
$$+194$$

Solution

Solution:- (A) $$-388$$
$$\Delta G^0=-nF E_{Cell}^0=-2\times 96500 \times 2.0\times 10^{-3}=-388kJ/mol$$
Question 4
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Assertion : A reaction which is spontaneous and accompanied by decrease of randomness must be exothermic.
Reason : All exothermic reactions are accompanied by decrease of randomness.

A
both assertion and reason are true and the reason is the correct explanation of assertion.

B
both assertion and reason are true but the reason is not the correct explanation of assertion.

C
assertion is true but reason is false.

D
both assertion and reason are false
Question 5
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In which case, process will be spontaneous at all temperatures?

A
$$\Delta H<0,$$ $$\Delta S>0$$

B
$$\Delta H>0,$$ $$\Delta S>0$$

C
$$\Delta H<0,$$ $$\Delta S<0$$

D
$$\Delta H>0,$$ $$\Delta S<0$$

Solution

Solution:- (A) $$\Delta{H} < 0$$ and $$\Delta{S} > 0$$
For spontaneous process $$\Delta G=\Delta H-T\Delta S$$
$$\because \Delta H<0$$
$$\Delta S>0$$
Question 6
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The heat energy of $$743J$$ is needed to raise the temperature of $$5$$ moles of an ideal gas by $$2K$$ at constant pressure. How much heat energy is needed to raise the temperature of the same mass of the gas by $$2K$$ at constant volume?

A
$$826J$$

B
$$743J$$

C
$$660J$$

D
$$600J$$

Solution

as we know,

$$(Q)_P=nC_PΔT=\Delta H$$

$$C_P−C_V=R⇒C_V=C_P−R,\ (Q)_V=nC_VΔT=\Delta U$$

At constant pressure,

$$\Delta H=nC_PΔT=743J$$

At constant volume,

$$\Delta U=nC_vΔT=n(C_p−R)\Delta T=nC_PΔT-nRΔT$$

$$\Delta U=743−(5×8.3×2)$$

$$\Delta U=660J$$

Option C is correct.
Question 7
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A student mixed 25.0cm3 of 4.00 moldm–3 hydrochloric acid with an equal volume of 4.00moldm–3 sodium hydroxide.?
The initial temperature of both solutions was 15.0°C. The
maximum temperature recorded was 30.0°C.
Using these results, what is the enthalpy change of neutralisation of hydrochloric acid?

A
$$-62.7kJ$$ $${mol}^{-1}$$

B
$$-31.4kJ$$ $${mol}^{-1}$$

C
$$-15.7kJ$$ $${mol}^{-1}$$

D
$$-3.14kJ$$ $${mol}^{-1}$$

Solution

Calculate heat absorbed by the water:
(Assume density of solutions = 1.00 g/cm^3 and specific heat of solution is the same as water)
q = m c (T2-T1)
q = 50 g (4.184 J/gC) ( 30-15 C) = 3138 J

Heat released by neutralization reaction = -3138 J
Moles HCl used = 0.0250 L X 4.00 mol/L = 0.100 mol

Delta H = -3138 J / 0.100 mol = -3.14X10^4 J = -31.4 kJ/mol
B is the correct answer.
Question 8
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For a system in equilibrium, $$\Delta G=0$$ under conditions of constant:

A
temperature and pressure

B
temperature and volume

C
pressure and volume

D
energy and volume

Solution

For a system in equilibrium $$\Delta G=0$$at constant pressure and temperature.

$$G(p,T)=U+PV-TS$$

$$G(p,T)=H-TS$$

So, Gibbs's free energy is defined for constant pressure and temperature.

Hence, the correct option is A
Question 9
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Directions For Questions

One mole of an ideal gas whose adiabatic exponent equals $$\gamma$$ undergoes a process in which the gas pressure relates to the temperature as $$p=a {T}^{\alpha }$$, where $$a$$ and $$\alpha $$ are constants

...view full instructions

At what value of $$\alpha$$ will the heat capacity be negative?

A
$$\alpha <-1$$

B
$$\alpha <0$$

C
$$\alpha >\cfrac { \gamma }{ \gamma -1 } $$

D
$$\alpha <\gamma \quad $$
Question 10
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What is the heat capacity of the ideal monoatomic gas undergoing the process shown in the figure?

A
$$1.5R$$

B
$$2.5R$$

C
$$3.5R$$

D
$$1.33R$$

Solution