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Question: How much heat in joules and in calories, must be added to a \(75gm\) iron block with specific heat o...

How much heat in joules and in calories, must be added to a 75gm75gm iron block with specific heat of 0.449J gm−1 oC−10.449J\,g{{m}^{-1}}\,{}^{o}{{C}^{-1}} to increase its temperature from 25oC{{25}^{o}}C to its melting temperature of 1535oC{{1535}^{o}}C?

Explanation

Solution

The specific heat is the heat required per gram to raise the temperature of a substance. The heat required to change the temperature of iron slab depends on the mass and change in temperature. We can substitute the corresponding values in the following relation to calculate heat. Joules and calories are different units used to express energy or heat.
Formulas used:
H=mcΔTH=mc\Delta T

Complete answer:
The specific heat of a substance is the heat required to increase the temperature of a substance by 1oC1{}^{o}C per unit mass. Therefore, it is given by-
H=mcΔTH=mc\Delta T
Here, HH is the heat given to the substance
mm is the mass
cc is specific heat
ΔT\Delta T is the change in temperature
Given, for an iron block, m=75gmm=75gm, c=0.449J gm−1 oC−1c=0.449J\,g{{m}^{-1}}\,{}^{o}{{C}^{-1}}, ΔT=1535−25=1510oC\Delta T=1535-25=1510{}^{o}C
We substitute given values in the above equation to get,
H=75×0.449×1510 ⇒H=50.85J \begin{aligned} & H=75\times 0.449\times 1510 \\\ & \Rightarrow H=50.85J \\\ \end{aligned}
Therefore, the heat required to increase the temperature of iron in joules is 50.85J50.85J.
The relation between joules and calories is-
1cal=4.2J1cal=4.2J - (1)
Using eq (1), we convert 50.85J50.85J into calories as-
x cal=50.85J4.2 ⇒x cal=12.11cal \begin{aligned} & x\,cal=\dfrac{50.85J}{4.2} \\\ & \Rightarrow x\,cal=12.11cal \\\ \end{aligned}
Therefore, the heat required in calories to change the temperature of iron slab is 12.11cal12.11cal.
Therefore, the heat required to change the temperature of iron slab to its melting temperature in joules is 50.85J50.85J and in calories is 12.11cal12.11cal.

Note:
To calculate the heat required to melt the iron slab, we will have to calculate its latent heat. To change the state of a substance, latent heat is used. The specific heat of a substance is constant, and is different for different substances. Specific heat can also be described as the heat capacity of a substance.