Answer to Question #223305 in Quantum Mechanics for Danfulde

Question

2.5kg of water is heated in an open container for 5 minutes using a heater of power 2KW. Which of the following statements about the temperature of the water is true?(the SHC of water= 4200Jkg^-1k^-1)

A. The change in temperature of the water is 58.3⁰C

B. The change in temperature of the water is 57.3⁰C

C. The change in temperature of the water is greater 57.3⁰C

D.If the initial temperature of the water was 23.7⁰C then its final temperature would be 810⁰C

Answer 1

The amount of heat required to change the temperature of the water can be found as follows:

$$Q=mc\Delta T.$$

From the other hand, we can write:

$$Q=Pt.$$

Equating these two expressions, we get:

$$mc\Delta T=Pt,$$ $$\Delta T=\dfrac{Pt}{mc},$$ $$\Delta T=\dfrac{2.0\times10^3\ W\times5\ min\times\dfrac{60\ s}{1\ min}}{2.5\ kg\times4200\ \dfrac{J}{kg\!\times\!^{\circ}C}}=57.3^{\circ}C.$$

As we can see from the calculations, the change in temperature of the water is $57.3^{\circ}C$. Therefore, the correct answer is (B).

Answer:

B. The change in temperature of the water is 57.3⁰C