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A substance of mass M kg requires a powe...

A substance of mass M kg requires a power input of P wants to remain in the molten state at its melting point. When the power source is turned off, the sample completely solidifies in time t seconds. The latent heat of fusion of the substance is …….

A

Pm/t

B

Pt/m

C

m/Pt

D

t/mc

Text Solution

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The correct Answer is:
To find the latent heat of fusion of a substance given its mass, power input, and the time taken to solidify, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Given Information**: - Mass of the substance = \( M \) kg - Power input required to keep the substance molten = \( P \) watts (which is equivalent to \( P \) joules/second) - Time taken to solidify after the power source is turned off = \( t \) seconds 2. **Heat Supplied to Keep the Substance Molten**: - When the power is on, the substance is kept in the molten state by supplying heat at the rate of \( P \) joules per second. 3. **Heat Released During Solidification**: - When the power source is turned off, the substance releases heat as it solidifies. The total heat released during the time \( t \) seconds can be calculated as: \[ \text{Total Heat Released} = P \times t \] - This heat released is equal to the latent heat of fusion of the substance. 4. **Relate Heat Released to Latent Heat**: - The latent heat of fusion (\( L \)) is defined as the amount of heat required to change a unit mass of a substance from solid to liquid (or vice versa) without a change in temperature. - For the mass \( M \), the total heat released can also be expressed as: \[ \text{Total Heat Released} = M \times L \] 5. **Set the Two Expressions for Heat Equal**: - From the above two points, we can set the expressions for total heat released equal to each other: \[ P \times t = M \times L \] 6. **Solve for Latent Heat of Fusion**: - Rearranging the equation to solve for \( L \): \[ L = \frac{P \times t}{M} \] ### Final Answer: The latent heat of fusion of the substance is given by: \[ L = \frac{P \times t}{M} \]
To find the latent heat of fusion of a substance given its mass, power input, and the time taken to solidify, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Given Information**: - Mass of the substance = \( M \) kg - Power input required to keep the substance molten = \( P \) watts (which is equivalent to \( P \) joules/second) - Time taken to solidify after the power source is turned off = \( t \) seconds ...
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