Answer:
The value is [tex]V = 900 \ cm^3[/tex]
Explanation:
From the question we are told that
The power output is [tex]P_{out} = 2.0 \ kW = 2.0 *10^{3} \ W[/tex]
The mass of the steel is [tex]m= 650 \ g = \frac{650}{1000} = 0.650 \ kg[/tex]
The temperature of the water is [tex]T = 20^o C[/tex]
The time take is [tex]t = 2.70 \ minutes = 2.70 *60 = 162 \ s[/tex]
Generally the quantity of heat energy given out by the electric stove is mathematically represented as
[tex]Q = P * t[/tex]
=> [tex] Q = 2.0 *10^{3} * 162[/tex]
=> [tex] Q = 324000 \ J [/tex]
This energy can also be mathematically represented as
[tex]Q = \Delta T * m c_s * + m_w * c_w * \Delta T[/tex]
Here [tex]c_s[/tex] is the specific heat of stainless steel with value [tex]c_s = 450\ J/C/kg[/tex]
tex]c_s[/tex] is the specific heat of water with value [tex]c_s = 4180\ J/C/kg[/tex]
m_w is the mass of water which is mathematically represented as
[tex]m_w = \rho_w * V[/tex]
=> [tex]m_w = 1000 * V[/tex]
So
[tex]324000 = (100 -20 ) * 0.650 * 450 * + 1000V * 4180 * (100-20)[/tex]
[tex]V = 0.0008989 \ m^3[/tex]
converting to [tex]cm^3[/tex]
[tex]V = 900 \ cm^3[/tex]
