The volume of iron will have the same thermal capacity as 1200 cal/°C of water if 16 × 10^x cc, x value is ......... (specific heat of iron = 0.1 cal/g°C, density of iron = 7.5 g/cc)
Answer (1)
To solve this problem, we need to find the volume of iron that has the same thermal capacity as 1200 cal/°C of water.
Step-by-step Solution:
Understand Thermal Capacity:
The thermal capacity is the amount of heat required to change the temperature of a substance by one degree Celsius (or Kelvin).
For water, thermal capacity = 1200 cal/°C.
Formula for Thermal Capacity:
Thermal capacity (C) can also be expressed as: C = m × c s where:
m is the mass of the substance.
c s is the specific heat capacity of the substance.
Thermal Capacity of Iron:
Let the volume of iron be V cc (cubic centimeters).
Given:
Specific heat of iron = 0.1 cal/g°C
Density of iron = 7.5 g/cc
Mass of the iron can be given by m = density × volume = 7.5 × V g
Calculate Thermal Capacity of Iron:
Thermal capacity of iron = m × c s = 7.5 × V × 0.1 cal/°C
C iron = 0.75 × V cal/°C
Equate to Water's Thermal Capacity:
Set the thermal capacities equal: 0.75 × V = 1200
Solve for V :
V = 0.75 1200 V = 1600 cc
Express in Given Form & Find x :
The expression is 16 × 1 0 x and it has to equal 1600.
Simplify 1600: 1600 = 16 × 100 = 16 × 1 0 2
Therefore, x = 2 .
Answer: The value of x is 2.
