Question

1

a) An electric range burner weighing 698.0 grams is turned off after reaching a temperature of 463.5°C, and is allowed to cool down to 22.0°C.

Calculate the specific heat of the burner if all the heat evolved from the burner is used to heat 593.0 grams of water from 22.0°C to 81.4°C.

b)An electric range burner weighing 698.0 grams is turned off after reaching a temperature of 478.0°C, and is allowed to cool down to 23.8°C.

Calculate the specific heat of the burner if all the heat evolved from the burner is used to heat 567.0 grams of water from 23.8°C to 80.4°C.

Answer 1

Answer 1-

a)

Given,

Mass of electric range burner = 698.0 g

Initial Temperature of electric range burner = 463.5 °C

Final Temperature of electric range burner = 22.0 °C

Mass of water = 593.0 g

Initial Temperature of water = 22.0 °C

Final Temperature of water = 81.4 °C

Specific Heat of water = 4.184 J/g˚C [KNOWN VALUE]

Specific Heat = ?

We know that,

Heat = m * s * (T_f - T_i)

where,

m = mass

s = specific heat

T_f = Final Temperature

T_i = Initial Temperature

Heat lost = - Heat gained

So,

According to the problem,

m_b * s_b * (T_f-b - T_i-b) = - m_w * s_w * (T_f-w - T_i-w)

m_b * s_b * (T_f-b - T_i-b) = m_w * s_w * (T_i-w - T_f-w)

Put the values,

698.0 g * s_b * (22.0 °C - 463.5 °C) = 593.0 g * 4.184 J/g˚C * (22.0 °C- 81.4 °C)

698.0 g * s_b * (- 441.5 °C) = 593.0 g * 4.184 J/g˚C * (- 59.4 °C)

- 308167 g°C * s_b = - 147378.0528 J

s_b = - 147378.0528 J/- 308167 g°C

s_b = 0.478 J/g°C [ANSWER]

b)

Given,

Mass of electric range burner = 698.0 g

Initial Temperature of electric range burner = 478.0 °C

Final Temperature of electric range burner = 23.8 °C

Mass of water = 567.0 g

Initial Temperature of water = 23.8 °C

Final Temperature of water = 80.4 °C

Specific Heat of water = 4.184 J/g˚C [KNOWN VALUE]

Specific Heat = ?

We know that,

Heat = m * s * (T_f - T_i)

where,

m = mass

s = specific heat

T_f = Final Temperature

T_i = Initial Temperature

Heat lost = - Heat gained

So,

According to the problem,

m_b * s_b * (T_f-b - T_i-b) = - m_w * s_w * (T_f-w - T_i-w)

m_b * s_b * (T_f-b - T_i-b) = m_w * s_w * (T_i-w - T_f-w)

Put the values,

698.0 g * s_b * (23.8 °C - 478.0 °C) = 567.0 g * 4.184 J/g˚C * (23.8 °C- 80.4 °C)

698.0 g * s_b * (- 454.2 °C) = 567.0 g * 4.184 J/g˚C * (- 56.6 °C)

-317031.6 g°C * s_b = -134273.7648 J

s_b = 0.423 J/g°C [ANSWER]