Answer:
The mass is [tex]m = 3.75 \ kg[/tex]
Explanation:
From the question we are told that
The initial temperature is [tex]T_1 = 15^oC[/tex]
The final temperature is [tex]T_2 = 100 ^o C \ (boiling point )[/tex]
Generally the maximum heat produced by 1 Liter of natural gas is [tex]9000 \ cal[/tex]
So the amount of heat produced by 100 L is
[tex]E = 9000 * 100[/tex]
=> [tex]E = 9000 00 \ cal[/tex]
Generally given that the efficiency is [tex]\eta = 0.35[/tex]
Then actual heat received by the water is
[tex]H = 0.35 * E[/tex]
=> [tex]H = 0.35 * 9000 00[/tex]
=> [tex]H = 315000 \ cal[/tex]
Converting to kcal
=> [tex]H = 315000 \ cal = \frac{315000}{1000} = 315 \ kcal[/tex]
Generally the specific heat of water is
[tex]c_w = 1 kcal/ kg \cdot ^oC[/tex]
Generally the heat received by the water is mathematically represented as
[tex]H = m * c_w * (T_2 - T_1)[/tex]
=> [tex]315 = m * 1 * ( 100 - 15 )[/tex]
=> [tex]m = 3.75 \ kg[/tex]
