Question 50: Thermodynamics & KTG

Question

An iron piece of mass $$200 \mathrm{~g}$$ is kept inside a furnace for some time and then put in a calorimeter of water equivalent $$20 \mathrm{~g}$$ containing $$230 \mathrm{~g}$$ of water at $$20 \mathrm{C}$$. The steady state temperature attained by the mixture is $$60^{\circ}$$. The temperature of the furnace is (Specific heat capacity of iron is $$470 \mathrm{~J~kg}^{-1} \mathrm{C}^{-1}$$ )

Accepted Answer

Let's solve the problem step by step.
The iron piece is heated in a furnace to a temperature $$T$$ (in ÃÂ°C) and then transferred to a calorimeter. After some time, the system equilibrates at $$60^{\circ}C$$.
When the iron (of mass $$200~g = 0.200~kg$$) is placed in the calorimeter, it cools from $$T$$ to $$60^{\circ}C$$. The energy lost by the iron is given by:
$$Q_{	ext{iron}} = m_{	ext{iron}}\,c_{	ext{iron}} \,(T - 60)$$
where
$$m_{	ext{iron}} = 0.200~kg$$,
$$c_{	ext{iron}} = 470~J\,kg^{-1}C^{-1}$$.
The calorimeter contains $$230~g$$ of water and has a water equivalent of $$20~g$$. The total effective mass of water is:
$$0.230~kg + 0.020~kg = 0.250~kg$$.
The water heats up from $$20^{\circ}C$$ to $$60^{\circ}C$$, a temperature rise of $$40^{\circ}C$$. The energy gained by the water and calorimeter is:
$$Q_{	ext{water}} = m_{	ext{eff}}\,c_{	ext{water}}\,(60 - 20)$$
where we use
$$m_{	ext{eff}} = 0.250~kg$$,
$$c_{	ext{water}} \approx 4200~J\,kg^{-1}C^{-1}$$.
According to the conservation of energy:
$$Q_{	ext{iron}} = Q_{	ext{water}}$$
Substituting the expressions:
$$0.200 	imes 470 	imes (T - 60) = 0.250 	imes 4200 	imes 40$$
First, calculate the constants:
For iron: $$0.200 	imes 470 = 94~J/^{\circ}C$$,
For water: $$0.250 	imes 4200 	imes 40 = 42000~J$$.
So, the equation becomes:
$$94(T - 60) = 42000$$
Solving for $$T$$:
$$T - 60 = \frac{42000}{94} \approx 446.81$$
$$T \approx 60 + 446.81 = 506.81^{\circ}C$$
Thus, the temperature of the furnace is approximately $$506.8^{\circ}C$$.
This corresponds to Option C.

Answer

464.7$$^\circ$$C

Answer

893.6$$^\circ$$C

Answer

506.8$$^\circ$$C

Answer

953.6$$^\circ$$C

Thermodynamics & KTG

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