Thermal Properties Of Matter

The rate of cooling of a liquid depends on its specific heat capacity. The liquid with a smaller specific heat capacity will lose heat faster. In this case, the ratio of specific heat capacities is 1 : 2 : 4 for liquids A, B, and C, respectively.
Liquid A has the smallest specific heat capacity, so it cools the fastest.
Liquid B has a medium specific heat capacity, so it cools slower than A but faster than C.
Liquid C has the largest specific heat capacity, so it cools the slowest. Thus, the correct answer is that B cools faster than C but slower than A.

The correct option is (B) : B cools faster than B but slower than A and (C): A cools faster than B and C

Given:

• An ideal gas is compressed in volume by a factor of 2 (V → V/2).
• The temperature (T) is kept constant during this process.
• We need to determine how the speed of sound in the gas changes.

Step 1: Speed of Sound in an Ideal Gas

The speed of sound (c) in an ideal gas is given by:

where:

• γ = adiabatic index (ratio of specific heats)
• R = universal gas constant
• T = absolute temperature
• M = molar mass of the gas

Step 2: Analyze the Given Conditions

Key observations:

1. The temperature T is constant (given).
2. γ, R, and M are properties of the gas that remain unchanged.
3. The volume change affects density, but not the speed of sound directly.

Step 3: Conclusion

Since none of the terms in the speed of sound equation (γ, R, T, M) are changing, the speed of sound remains unchanged despite the volume compression.

Final Answer: The speed of sound in the gas is unchanged.

Answer:

Given parameters:

• Initial velocity
• Initial temperature
• Melting point
• Specific heat
• Latent heat

Initial kinetic energy:

Heat required for temperature rise:

Heat required for melting:

Total heat generated:

Ratio calculation:

Thus, the correct option is (B): .