Final answer:
To find the time required by a surgical cauterizer to heat and vaporize tissue, calculate the energy needed for each process using the specific heat capacity and heat of vaporization, respectively. Then, convert the cauterizer's power output to watts and divide the total energy by the power to get the time.
Step-by-step explanation:
To determine how much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from 37.0°C to 100°C and then boil away 0.500 g of water with a power output of 2.00 mA at 15.0 kV, we need to calculate the energy required for both heating the tissue and vaporizing the water, and then find out how long it will take for the cauterizer to provide this energy.
First, to heat 1.00 g of tissue from 37.0°C to 100°C, we will assume that tissue's specific heat capacity is similar to that of water, which is 4.18 J/g°C. The energy required (Q) for this step can be calculated using the formula Q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Q = (1.00g)(4.18J/g°C)(100°C - 37.0°C).
Second, to vaporize 0.500 g of water, we use the heat of vaporization for water, which is 2260 J/g. Therefore, the energy required for vaporization is Q = (0.500 g)(2260 J/g).
To find the total energy needed, we add the amounts from both processes. Then, we convert the cauterizer's power output from milliamps and kilovolts to watts (W = IV), where I is current and V is voltage. Next, we divide the total energy by the power to get the time, t, using the formula t = Q / P.
Remember that the power output of the cauterizer should first be converted to watts, which is the standard unit for power in the calculation (1W = 1A * 1V). Thus, the power P in watts is P = (2.00 mA * 10^-3 A/mA) * (15.0 kV * 10^3 V/kV).