Server energy consumption has been a subject of research for more than a decade now. With Internet scaling rapidly all over the world, more servers are being added continuously. With global warming and financial cost associated with running servers, it has now become a more pressing concern to optimize the power consumption of these servers while still not affecting the performance. The optimization that can be carried out at the hardware level has its limits and therefore the onus comes on to the software developers as well to optimize their web interacting services and use protocols that are more efficient. Recently, Internet Engineering Task Force (IETF) formalized the specification for the successor of HTTP/1.1 protocol. Named HTTP/2, it has been projected to overcome all the limitations of HTTP/1.1 protocol for which web services developers have to optimize their applications. Understandably, HTTP/2 has been drawing a lot of interest from users, web administrators to big organizations. With HTTP/2 as the future of the Internet communication and servers acting as the backbone of the Internet, we are interested in knowing if HTTP/2 will provide energy efficiency benefits to servers or it will just improve users web experience. In this paper, we evaluate the energy efficiency of two web servers while they communicate over HTTP/1.1 and HTTP/2 protocol. We also investigate how Transport layer security (TLS) affects the power consumption of the servers. In our tests, we have introduced HTTP/2 features one by one so that readers can see for themselves what benefits the HTTP/2 over HTTP/1.1. Our study suggests that multiplexing and Round Trip time (RTT) are the biggest factors helping HTTP/2 achieve its design goals. We conclude that even with huge TLS associated cost with HTTP/2, on high latency networks it can help servers to be more energy efficient while improving their performance as well.