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 Homework Statement

The source question is very long, and most likely unneeded. This question is about an actual refrigeration cycle. For the first part of the question, I'm to use the given isentropic efficiency to calculate ##h_{2s}##.
##P_1=140~kPa##
##T_1=10°C##
##P_2=1~MPa##
##\eta = 0.78##
 Homework Equations
 ##\eta=\frac {h_{2s}h_1} {h_2  h_1}##
A short background: My question focuses solely on the part of the refrigeration cycle to do with the compressor, where the cycle begins. The first state is before the refrigerant enters the compressor, and the second state is after the refrigerant leaves the compressor. My goal is to obtain ##h_2##; but for that, I need ##h_{2s}##.
From the Thermodynamic Tables:
##h_1=h(140~kPa,~10°C)=246.37~kJ/kg##
Easy enough to obtain. All that's left is ##h_{2s}##. From the Ts diagram of the refrigeration cycle, it can be seen that:
##s_{2s}=s_1##
##s_1=s(140~kPa,~10°C)=0.9724~kJ/kg\cdot K##
So I know that the entropy at state ##2s## is ##0.9724~kJ/kg\cdot K##
Now this is where I'm stuck. I don't know how to get ##h_{2s}##.
State 1 I know for sure the refrigerant is superheated. And state 2, I'm near to certain it's still superheated.
In other questions, I've been able to work out ##h_{2s}## when state 2 is a mixture. I use the entropies to work out quality,
##x=\frac {ss_f} {s_{fg}}##
And then knowing the quality, work out ##h_{2s}##:
##h_{2s}=x(h_{fg})+h_f##
I can't do that though if they're both superheated. There's no, 'quality' or, 'x', nor any saturated liquid values. This has come up once before this time, and I was unable to answer it then too. Any help would be appreciated.
From the Thermodynamic Tables:
##h_1=h(140~kPa,~10°C)=246.37~kJ/kg##
Easy enough to obtain. All that's left is ##h_{2s}##. From the Ts diagram of the refrigeration cycle, it can be seen that:
##s_{2s}=s_1##
##s_1=s(140~kPa,~10°C)=0.9724~kJ/kg\cdot K##
So I know that the entropy at state ##2s## is ##0.9724~kJ/kg\cdot K##
Now this is where I'm stuck. I don't know how to get ##h_{2s}##.
State 1 I know for sure the refrigerant is superheated. And state 2, I'm near to certain it's still superheated.
In other questions, I've been able to work out ##h_{2s}## when state 2 is a mixture. I use the entropies to work out quality,
##x=\frac {ss_f} {s_{fg}}##
And then knowing the quality, work out ##h_{2s}##:
##h_{2s}=x(h_{fg})+h_f##
I can't do that though if they're both superheated. There's no, 'quality' or, 'x', nor any saturated liquid values. This has come up once before this time, and I was unable to answer it then too. Any help would be appreciated.