Question

The specific heat of a substance at its boiling point or melting point
Is 0
Is infinity
Is negative
lies between 0 and 1
2 A unit mass of solid converted to liquid at its melting point. Heat is required for this process is
Specific heat
Latent heat of vaporization
Latent heat of fusion
External latent heat
3 At a certain temperature, hydrogen molecules have r.m.s. velocity of 3 km/s. what is the r.m.s velocity of the oxygen molecules at the same temperature?
0.25 km/s
0.5 km/s
0.75 km/s
0.6 km/s
4 Which one of the following quantities can be zero on a average for the molecules of an ideal gas in equilibrium?
Kinetic energy
Density
Momentum
Speed

Answer 1

Answer on Question #51927-Physics-Field Theory

The specific heat of a substance at its boiling point or melting point

Is 0

Is infinity

Is negative

lies between 0 and 1

Solution

The specific heat of a substance at its boiling point or melting point is infinity, because $\Delta T = 0$ but $\Delta Q \neq 0$ at these points in the formula for specific heat:

$$C = \frac{\Delta Q}{m \Delta T} \sim \frac{1}{\Delta T} \rightarrow \infty.$$

Answer: infinity.

2 A unit mass of solid converted to liquid at its melting point. Heat is required for this process is

- Specific heat

- Latent heat of vaporization

- Latent heat of fusion

- External latent heat

Solution

**Latent heat of fusion** is the amount of heat required to convert a unit mass of a solid at its melting point into a liquid. Thus, Heat is required for this process is **latent heat of fusion**.

Answer: Latent heat of fusion.

3 At a certain temperature, hydrogen molecules have r.m.s. velocity of $3\,\mathrm{km/s}$ what is the r.m.s velocity of the oxygen molecules at the same temperature?

- $0.25\,\mathrm{km/s}$

- $0.5\,\mathrm{km/s}$

- $0.75\,\mathrm{km/s}$

- $0.6\,\mathrm{km/s}$

Solution

The formula for r.m.s. velocity is

$$v_{rms} = \sqrt{\frac{3RT}{M}},$$

where $M$ is molar mass of gas, $T$ is temperature, $R$ is gas constant.

So,

$$\frac{v_{rms}(O_2)}{v_{rms}(H_2)} = \sqrt{\frac{M(H_2)}{M(O_2)}}.$$

Thus, the r.m.s velocity of the oxygen molecules is

$$v_{rms}(O_2) = v_{rms}(H_2) \sqrt{\frac{M(H_2)}{M(O_2)}} = 3 \frac{\mathrm{km}}{\mathrm{s}} \sqrt{\frac{2}{32}} = 0.75 \frac{\mathrm{km}}{\mathrm{s}}.$$

Answer: $0.75 \frac{\mathrm{km}}{\mathrm{s}}$.

4 Which one of the following quantities can be zero on an average for the molecules of an ideal gas in equilibrium?

- Kinetic energy

- Density

- Momentum

- Speed

Solution

Average momentum of the molecules of an ideal gas in equilibrium can be zero, because it depends of direction and when we take an average:

$$\langle \vec{p} \rangle = \frac{\sum \vec{p}_i}{N} = \vec{0}.$$

It is because that all directions are equivalent.

Answer: Momentum.

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