A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 400 kJ. During the process, hydrogen behaves as an ideal gas with constant specific heats. The absolute value of heat transfer during the process is ____________ kJ (rounded off to 1 decimal place).

Specific heat of hydrogen at constant pressure = 14.56 kJ kg^-1 K^-1

Specific heat of hydrogen at constant volume = 10.4 kJ kg^-1 K^-1

The correct answer is 100.0 kJ (or 100).

Here is the step-by-step educational explanation of the solution:

1. Identify the given data:
Mass of hydrogen, $m=1\text{kg}$
Polytropic index, $n=1.3$
Work output, $W=400\text{kJ}$
Specific heat at constant pressure, $C_p=14.56{\text{kJ kg}}^{-1}{\text{K}}^{-1}$
Specific heat at constant volume, $C_v=10.4{\text{kJ kg}}^{-1}{\text{K}}^{-1}$

2. Calculate the ratio of specific heats ($\gamma$):
The ratio of specific heats is defined as:
$$\gamma =\frac{C_p}{C_v}$$
Substituting the given values:
$$\gamma =\frac{14.56}{10.4}=1.4$$

3. Use the relationship between Heat Transfer and Work Done in a Polytropic Process:
For an ideal gas undergoing a reversible polytropic process, the heat transfer ($Q$) is related to the polytropic work output ($W$) by the following relation:
$$Q=W\times \left(\frac{\gamma -n}{\gamma -1}\right)$$

4. Substitute the values to find the heat transfer:

$$Q=400\times \left(\frac{1.4-1.3}{1.4-1}\right)$$
$$Q=400\times \left(\frac{0.1}{0.4}\right)$$
$$Q=400\times 0.25=100.0\text{kJ}$$

Thus, the absolute value of heat transfer during the polytropic process is 100.0 kJ.