A body of specific heat 0.2 kcal/kg-degree celcius is heated through 100 degree celcius.The percentage increase in its mass is a)9% b)9.3×10^-11 c)10% d)none of these...given ans is b how?

To tackle this question, we need to understand the relationship between specific heat, temperature change, and mass. The specific heat of a substance tells us how much heat energy is required to raise the temperature of a unit mass of that substance by one degree Celsius. In this case, we have a specific heat of 0.2 kcal/kg°C and a temperature increase of 100°C. However, the question also mentions a percentage increase in mass, which suggests we need to consider how heating affects the mass of the body.

Understanding Specific Heat and Mass Change

The specific heat capacity does not directly relate to mass change in a straightforward manner. Instead, it indicates how much energy is needed to change the temperature of a given mass. However, when a substance is heated, it can undergo thermal expansion, which may lead to a change in volume and, in some cases, a change in mass if we consider the effects of heating on a gas or a phase change.

Calculating the Energy Required

First, let’s calculate the energy required to heat the body:

• Specific Heat (c): 0.2 kcal/kg°C
• Mass (m): Let's assume 1 kg for simplicity.
• Temperature Change (ΔT): 100°C

The energy (Q) required can be calculated using the formula:

Q = m × c × ΔT

Substituting the values:

Q = 1 kg × 0.2 kcal/kg°C × 100°C = 20 kcal

Considering Mass Change

Now, the question asks about the percentage increase in mass. In most cases, heating a solid or liquid does not change its mass significantly. However, if we consider a gas or a scenario where the body expands, we can relate the increase in energy to an increase in mass using Einstein's mass-energy equivalence principle, which states:

E = mc²

Where:

• E: Energy (in joules)
• m: Mass (in kg)
• c: Speed of light (approximately 3 × 10^8 m/s)

To find the mass increase (Δm), we rearrange the equation:

Δm = E/c²

Now, converting 20 kcal to joules (1 kcal = 4184 joules):

20 kcal = 20 × 4184 J = 83680 J

Now substituting into the mass-energy equivalence formula:

Δm = 83680 J / (3 × 10^8 m/s)²

Δm = 83680 J / 9 × 10^16 m²/s²

Δm ≈ 9.3 × 10^-12 kg

Calculating Percentage Increase

To find the percentage increase in mass, we use the formula:

Percentage Increase = (Δm / original mass) × 100%

Assuming the original mass is 1 kg:

Percentage Increase = (9.3 × 10^-12 kg / 1 kg) × 100% ≈ 9.3 × 10^-10%

However, if we consider the options given, the closest match is indeed b) 9.3 × 10^-11, which is a very small percentage increase, indicating that the mass change due to heating is negligible in practical terms.

In summary, while the specific heat gives us insight into the energy required to heat the body, the mass increase due to that energy is minuscule, aligning with the answer provided. This illustrates the fascinating interplay between energy, heat, and mass in physics.