Question

You have two equivalent pots a and b with one liter and three liters of water respectively. both pots begin at 25 c then the same amount of heat is added to each pot. the three liter pot's final temperature is 35

c. what is the final temperature of the one liter pot?

Answer 1

55 C

Step-by-step explanation:

When a certain substance is heated, the temperature of the substance increases according to the equation

`Q=mC\Delta T`

where

Q is the heat supplied to the substance

m is the mass of the substance

C is the specific heat of the substance

`\Delta T` is the change in temperature of the substance

The equation can be rewritten as

`\Delta T=(Q)/(mC)`

In this problem, the two pots both contain water, so the specific heat (C) is the same. Also, the same amount of heat is supplied, so Q is the same.

However, pot A contains 1 liter of water, while pot B containes 3 liters: this means that the mass of water in pot B is 3 times the mass of water in pot A,

`m_B = 3 m_A`

Since
`\Delta T` is inversely proportional to the mass, this means that

`\Delta T_A=3\Delta T_B`

The change in temperature of the water in pot B is

`\Delta T_B=35C-25C=10C`

So, the change in temperature of the water in pot A is

`\Delta T_A=3\Delta T_B=3(10)=30C`

So, the final temperature of pot A is

`T_A =T_0+\Delta T_A=25C+30C=55C`