55 kJ of heat are added to 200 kg of a metal at 28.00◦C and the temperature rises to 29.18◦C. What was the metal?
1. tungsten (specific heat = 0.134 J/g ·
◦ C)
2. copper (specific heat = 0.385 J/g ·
◦ C)
3. silver (specific heat = 0.233 J/g ·
◦ C)
4. lead (specific heat = 0.127 J/g ·
◦ C)
lead
Silver
To determine the metal, we can use the formula:
q = mcΔT
Where q is the heat absorbed or released by the metal, m is the mass of the metal, c is the specific heat capacity of the metal, and ΔT is the change in temperature.
First, let's convert the specific heat capacity from J/g·°C to J/kg·°C. Since we have the mass of the metal in kilograms (200 kg), this conversion will be necessary.
1. Tungsten: 0.134 J/g·°C = 134 J/kg·°C
2. Copper: 0.385 J/g·°C = 385 J/kg·°C
3. Silver: 0.233 J/g·°C = 233 J/kg·°C
4. Lead: 0.127 J/g·°C = 127 J/kg·°C
Now, we can substitute the values into the formula:
q = mcΔT
55 kJ = (200 kg)(c)(29.18°C - 28.00°C)
Simplifying further:
55,000 J = 200(c)(1.18°C)
Dividing both sides of the equation by 200 and 1.18:
275 J/kg = c
Comparing this value with the specific heat capacities of the metals:
1. Tungsten: 134 J/kg·°C ≠ 275 J/kg
2. Copper: 385 J/kg·°C ≠ 275 J/kg
3. Silver: 233 J/kg·°C ≠ 275 J/kg
4. Lead: 127 J/kg·°C ≠ 275 J/kg
None of the specific heat capacities match the value of 275 J/kg, so none of the provided metals is the correct answer.
q = mass metal x specific heat x (Tfinal-Tinitial)
Solve for specific heat and compare in tables.