# Calculate the heat transferred when a 8 g of the iron nail is cooled from 50 degree C to 18...

## Question:

Calculate the heat transferred when a 8 g of the iron nail is cooled from {eq}50^{\circ}C {/eq} to {eq}18^{\circ}C {/eq}. The specific heat of iron is 0.45 {eq}J/g^{\circ}C {/eq}.

## Heat Transfer:

The heat transferred from one substance to another can be quantified from the measured change in temperature of one substance. The heat transfer equation can be written as {eq}\displaystyle q = mc\Delta T {/eq}, where {eq}\displaystyle m {/eq} is the mass, {eq}\displaystyle c {/eq} is the specific heat, and {eq}\displaystyle \Delta T {/eq} is the change in the temperature of the material.

Determine the total heat transferred, {eq}\displaystyle q {/eq}, by the nail using the equation, {eq}\displaystyle q = mc\Delta T {/eq}, where {eq}\displaystyle m =8\ g {/eq} is the mass, {eq}\displaystyle c = 0.45\ \rm{J/g ^\circ C} {/eq} is the specific heat, and {eq}\displaystyle \Delta T = 18^\circ C - 50^\circ C =- 32 ^\circ C {/eq} is the change in temperature. We proceed with the solution.

{eq}\begin{align} \displaystyle q &= mc\Delta T\\ &= 8\ g\times 0.45\ \rm{J/g ^\circ C}\times -32 ^\circ C\\ &= -115.2\ J \end{align} {/eq}

The heat transferred is {eq}\displaystyle -115.2\ J {/eq}. The negative sign signifies that the nail lost heat.